I came across this conundrum years ago in my phonetics class in university.
Although the consonant blend 'tr' is pronounced [tʃɹ] as in 'tree' [tʃɹi:] in American English, I was taught that 'tw' is always pronounced [tw] as in 'tweet' [twi:t]. However, I view my own (native) pronunciation similarly to [tʃw].
Am I taking this out of nowhere? It concerns me as I'm beginning to teach phonics myself and I want to make sure I'm not teaching an incorrect pronunciation.
My one guess would be possibly that as a child I combined /w/ and /ɹ/ as a child, and the 'tr' change carried through even after I separated /w/ and /ɹ/. For reference, I'm a young adult, born and raised in the American South.