Am I allowed to use a passport from another country if using my US passport would require a visa?

It shouldn't be a problem. Use your Tunisian and American passport when checking in and clear passport control in Turkey with your Tunisian passport. On your exit in Turkey, check in with your American passport, pass border control in Turkey with your Tunisian passport and enter the US on your USA passport.

Of course it's allowed. Dual nationality is permitted under US law and the US thus has no say in what passport you use elsewhere.

If checking the stamps, the US official might ask if you hold another passport, in which case you simply say yes and show the Tunisian passport if asked (sometimes happens, but is no cause for concern)

Neither of the current answers has addressed your last question, so I will do so.

Would it be a problem if I used the Tunisian passport I when entering Turkey

As covered elsewhere, no.

would this cause problems when I come back to the US and go through customs?

It will not cause problems.

Would I have to tell US customs that I went to Turkey

Yes, you will have to tell them that. The customs declaration form requires you to list all of the countries you've visited on your trip. Omitting Turkey from your declaration could get you in trouble, but listing Turkey won't have any adverse consequence.

or no since I would be using my Tunisian passport?

It doesn't matter what passport you used; if you have been in Turkey, you have to tell them that. The reason they ask is because they're interested in the goods you might be carrying; that has nothing to do with which passport you will have used to enter Turkey.

Yes, I hold multiple citizenship and I do this all the time in order to avoid paying for a visa in certain countries.