I mentioned before that none of my teachers have ever noticed when I used
Liberation Serif. I imagine Tinos is similarly difficult to distinguish
FreeSerif, though, I know from observation is quite different, so there's no
way it would pass.
If your teacher is being a nitpick about it, I'd say don't just give up
there; insist on them accepting these almost metrically identical fonts like
Liberation Serif.
One other possible tactic, if a teacher stubbornly believes that everyone has
Times New Roman, is you can tell (and show) them that Liberation Serif is
"your Times New Roman" (because LibreOffice uses Liberation Serif if you tell
it to use Times New Roman). I would say that this is only an acceptable
choice if your teacher is particularly stubborn; it would be far better for
them to actually understand that some people just don't have the same fonts
they do.