I can not confirm or deny what your grandfather told you but there could be some truth to it.
I do know that the manifests were written at the port of departure from a document that our ancestor presented to the shipping clerk so TYSZKO must have been on the document, right.
As much as we want to be born in a big city like Kiev, we actually want our ancestors to be from a small village, much easier research than a large city .
Small number of TRECIAKs arriving NY EI
Not many TRECIAKs in Poland:http://www.moikrewni.pl/mapa/kompletny/treciak.htmlhttp://www.moikrewni.pl/mapa/kompletny/tretiak.html
To me TYSZKO looks Polish and TYSHKO americanized version as to have same pronouncation. If I would see your TYSHKO in Cyrillic than I would say Russian spelling. http://ua.translit.cc/