LeighAnn I have some watercolor tube paints----a few different companies too and none smell like turpentine or chemically (for lack of a better word). Some colors DO have a smell that reminds me more of chalk or dirt perhaps and other colors do have a weird smell (that to me stinks), but none that I can remember have that "shoot-up-your-nose" smell/feeling like turpentine or ammonia does to me. I would not be able to use them if they did!
If you cannot/don't want to take them back, then I would perhaps get a piece of wax paper/parchment paper/old plate no longer going to eat off of and you can squirt out a little of each colors to make a pallette and then let them air dry in another room/outside and then use later---it might get rid of the smell….but then the smell might also get "reactivated" when wetted again----and to contribute to my long run-on sentence-----this suggestion might also void the whole point of buying the tube paints to begin with.

Though tube paints are suppose to be richer I have read so it might not be so bad if you have to let them air-dry before use…any leftover watercolor paint I "squirted" out of the tube I just leave and use later on.