I have entered Turkey about five times using an e-Visa (most recently in June, twice), and have never been asked about/showed any proof of onward travel at all... just handed over the printout of the e-Visa with my passport. Both times in June I was in transit, LHR-IST-ABJ and ACC-IST-LHR, so not dissimilar to your wife's itin.

Now, I don't remember ever seeing the last line you quote (about travel on TK, Pegasus, Onur), so I'm guessing that is either nationality specific (I am a UK passport holder) or recently introduced, post-coup attempt, but I think it is beyond unlikely that your wife will have any problems.