There are surnames with -uk ending in certain regions of Poland and Ukraine (and Belarus as well). I would be careful with assuming that the surname ends with -yk, since it’s written with “u”.
I never heard about the surname “Tworczuk” though, I heard about “Sworczuk” instead and I know people with that surname.
Your example suggests the surname “Tworyczuk”, but I don’t know that neither.
The surnames with that ending are typical for Eastern Poland and Western Ukraine. Not sure if it’s common in Belarus, but I saw some people with surnames with this ending.