Are Chinese native speakers more sensitive to tones or phonemes? It seems like people are more sensitive to tones instead of phonemes. People may not notice some vowels/consonants are wrong but will immediately find that  tones are weird. Does this apply for all tonal languages?
Yes. It is not unusual for native Chinese to have difficulties distinguishing between nasal vs non-nasal or alveolars vs retroflexed, but I have never met someone who has difficulties distinguishing between the 4 tones in Mandarin. Though I am learning Cantonese right now and for me, a native Mandarin-speaking Chinese the 6 tones of Cantonese is a little bit tricky. I can't answer if this is true with regards to all tone languages, just my observation. Hope it helps