What is the purpose of "到" in 他在行窃时被当场抓到 I'm confused about 到 which means to arrive, or up until. How does it fit into the sentence "He was(is) caught in the act of stealing. " Also, how is past tense indicated here?
Your two questions answer each other! When 到 follows a verb, it indicates that the action has successfully completed. In linguistic terminology, it's sometimes referred to as indicating "completive aspect".

However, when you ask "how is past tense indicated here?", you should be aware that Mandarin doesn't always indicate past tense.  There are a number of aspect markers (including 了、到、过), but none of these directly correspond to English past tense.