I don't think it would be possible or practical to try and "invent" these other cultures whole-cloth, and expect them to be on par with your Europe-analagous area.
So, it would make sense to make the other cultures analagous to other real life cultural regions. Thus, your question is - how to treat them without resorting to ugly stereotypes.
Perhaps you could study sources from their own cultures, and see how they themselves write about their cultures.