Cotton is very porous therefore takes colours easier than poly which is much smoother. You will find the same distinction on some fabric dyes. It is MUCH easier to dye cotton than poly. One of poly’s biggest selling points is that everything washes out.

It takes different chemicals to make things ‘stick’ to poly than cotton, which is why there is a distinction on the papers.

I think your t’s should be fine. Wash 1 as normal (or by hand if you’re scared) to test before you wash the rest. That will be the only way of truly knowing how colourfast it is. Hopefully there were washing instructions on the transfer paper. Next time, try to wash the t’s first in order to get the ‘sizing’ out which will also aid the colour retention. Good luck!