I believe the average life of a street cat in Turkey is about 3 years.
In the short term, if those cats are actually getting nutrition and medical attention, one would expect that lifespan to both increase and be somewhat better quality. That increased lifespan will mean temporarily more cats - hence perhaps your perception that the 'problem' is worse, - together with the fact they arent hiding away in pain, injured, starving etc so are now more visible and congregating in safer colonies.
In the medium and long term, as those same cats will have been neutered the number of strays will fall drasticly. The only other action required to solve the long term problem is to EDUCATE locals from a young age that animals must be neutered and cared for properly, and that having acquired a pet it is a responsibility for the whole of its life.
getting an Animal 'put to sleep' is not that easy in Turkey, to put a healthy stray to sleep would not be considered appropriate in the local culture.
Sadly i also know some expats just turf animals out whe they return to the uk.
I am not an AA member but the work they have done with street animals has made a big difference to the dog situation, give them time and a little patience to work with the cats!