So we got on the IST-AMM flight fine. When on the flight, the flight into display showed the time in Amman as one hour earlier than IST, while Amman time is actually the same as IST. At least TK did inform us of the "operation change", of the corrected arrival time (of 23:10 instead of 22:10) just a few days before actual flight.

Separately, if anyone googles Jordan or Amman time, it shows something weird, something 5 hours off.