Is it permissible to pray in the Turkish mosque that calls the 'Isha prayer at 22:10, while the Islamic Center in Vienna calls it at 22:29?

The times for prayer are known only by cosmic signs, and the time for Isha begins with the disappearance of the red twilight. If the mosque congregation prays Isha after its time has begun, then pray with them. However, if they pray before the time has begun, your prayer with them will not be valid, because the entry of the time is a condition for the prayer's validity.