What record is there of a canon of Scripture having been set at the First Ecumenical Council? According to this synopsis


  As to Judith, he notes that the Council of Nicæa had, contrary to the Hebrew tradition, included it in the Canon of Scripture, and this, with his friends’ requests, had induced him to undertake the labour of emendation and translation.


by the editors of the Nicene and Post-Nicene series, Jerome wrote in his introduction to the Books of Tobit and Judith that that he was including Tobit in his Latin translation because it had been included in the canon by the Council of Nicea.

Assuming (a) that the synopsis is accurate (I can't find the full document); and (b) he means the First (Ecumenical) Council at Nicea in 325 (the second Nicean Council was in 787 - long after Jerome's death), which canons or acts are recorded that refer to the canon of Scripture?  I can find none.

We know from the Apostolic Canons (Canon LXXXV) and from the Canons of the local Council at Carthage in 397, that most of the deuterocanonical books were included in the Old Testament canon, but I can find no record of this being affirmed by the First Ecumenical Council. It also seems odd to me that Carthage would have issued Canons related to the Scriptural canon in 397 if Nicea had already issued such a canon in 325.  It similarly would not have made any sense for the eastern Fathers to have issued the Scriptural canon they did at the Council of Trullo in 692 (which also included the deuterocanonical books), nor for the 7th Ecumenical Council to have issued their Scriptural canon in 787 (which confirmed the Carthage and Trullo canons).
tl;dr: There is no record of the Council of Nicaea defining the Canon of Scripture. It is not clear what Jerome meant.

The Catholic Encyclopedia's entry for the Book of Judith summarizes what we know, stating


  St. Jerome, while rejecting in theory those books which he did not find in his Hebrew manuscript, yet consented to translate Judith because "the Synod of Nicaea is said to have accounted it as Sacred Scripture" (Praef. in Lib.). It is true that no such declaration is to be found in the Canons of Nicaea, and it is uncertain whether St. Jerome is referring to the use made of the book in the discussions of the council, or whether he was misled by some spurious canons attributed to that council.


This confirms as you well-observed that the 20 Canons of Nicaea(20 by some countings) do not define the extents of Scripture. Likewise, it is not contained in the Symbol. The Synodal Letter summarizing the acts of the council to the bishops of Egypt, Libya, and Cyrenaica does not mention it either. Together, these seem to indicate that the Council of Nicaea did not consider the matter. 

We are left to speculate why Jerome stated that the Council accounted Judith as Scripute. One possiblity is that Jerome simply made it up. This is perhaps the least satisfying and does not seem to fit the evidence. Consider what he wrote in his preface to Judith:


  Among the Jews, the book of Judith is considered among the apocrypha; its warrant for affirming those [apocryphal texts] which have come into dispute is deemed less than sufficient. Moreover, since it was written in the Chaldean [Old Aramaic] language, it is counted among the historical books. But since the Nicene Council is considered to have counted this book among the number of sacred Scriptures, I have acquiesced to your  request (or should I say demand!): and, my other work set aside, from which I was forcibly restrained, I have given a single night's work , translating according to sense rather than verbatim. I have hacked away at the excessively error-ridden panoply of the many codices; I conveyed in Latin only what I could find expressed coherently in the Chaldean words. Receive the widow Judith, example of chastity, and with triumphant praise acclaim her with eternal public celebration. For not only for women, but even for men, she has been given as a model by the one who rewards her chastity, who has ascribed to her such virtue that she conquered the unconquered among humanity, and surmounted the insurmountable.


It seems that Jerome was neither fond of the book nor keen on translating it. Inventing a canon to create more work for himself sounds unlikely. It is also possible, as the CE points out, that Jerome was mistaken about the canons of Nicaea. While not impossible, there is no record of such a false canon. Others have suggested (an unfortunately I cant't remember where I first heard it) that Jerome was speaking of the fifty copyies of the Bible that Constantine ordered to be made. But this theory runs into two significant challenges. Constantine's commision is dated to 331, serveral years after the Council. Second, it is not clear if the Sacred Scriptures ordered by Constantine contained the entire Bible (including the Deuterocanon) or a subset, perhaps the New Testament or Gospels alone. As with the spurious canon, this suggestion is possible but not well supported by evidence.

The CE suggest one other possibility:


  and it is uncertain whether St. Jerome is referring to the use made of the book in the discussions of the council


To me, this seems the most likely -- that one or more of the Nicaea Fathers used quotations from Judith to support an argument. To see my reasoning, consider what Jerome wrote in his Preface to Tobit.


  I do not cease to wonder at the constancy of your demanding. For you demand that I bring a book written in Chaldean words into Latin writing, indeed the book of Tobias, which the Hebrews exclude from the catalogue of Divine Scriptures, being mindful of those things which they have titled Hagiographa. I have done enough for your desire, yet not by my study. For the studies of the Hebrews rebuke us and find fault with us, to translate this for the ears of Latins contrary to their canon. But it is better to be judging the opinion of the Pharisees to displease and to be subject to the commands of bishops. I have persisted as I have been able, and because the language of the Chaldeans is close to Hebrew speech, finding a speaker very skilled in both languages, I took to the work of one day, and whatever he expressed to me in Hebrew words, this, with a summoned scribe, I have set forth in Latin words. I will be paid the price of this work by your prayers, when, by your grace, I will have learned what you request to have been completed by me was worthy. 


As with Judith, Jerome does not seem overly thrilled with translating Tobit. Unlike Judith, he agrees to do it because he finds it better to submit to bishops than Pharisees rather than pointing to a canon from Nicaea. While it is possible that a Nicaea set a canon including Judith but excluding Tobit, but that seems unlikely. More likely, some argument during the council used Judith, but Tobit was not relevent at any point. If I might be allowed to continue to speculate, note that the subject of clerical celibacy was discussed. (See also Canon III). Given what Jerome wrote about Judith:


  Receive the widow Judith, example of chastity, and with triumphant praise acclaim her with eternal public celebration. For not only for women, but even for men, she has been given as a model by the one who rewards her chastity, who has ascribed to her such virtue that she conquered the unconquered among humanity, and surmounted the insurmountable.


Perhaps the Book of Judith came up in this matter.