They were mostly athenean settlers, which is why when Persia conquered them, they asked Athens for help. Athens helped them but the ionian revolt failed and Persia was super pissed. The persian emperor had his servant reminding him daily to "remember the athenians".

This is the main reason behind the persian invasion of mainland Greece. The persians burnt Athens to the ground, which eventually led to Alexander the OK burning Persepolis(Persian Empire's Capital) to the ground(a couple centuries later).

Since turks came from the East, Ionians were kinda the first greeks they met, so they decided that all greeks are Ionians(Yunans). Or other non greeks in the East were already calling greeks "yunans" and turks just adopted that terminology too. Especially since that term had been mostly depreciated by the time the turks arrived to the neighbourhood.