As long as it is time to start the class I think it doesn't really matter - you or the teacher can call. I am a teacher and I usually call the student but sometimes the student calls me a few minutes before the class and it is not a problem.

Does it matter? Don't be shy, pick up the phone and give 'em a ring! :P

Usually I like to ask “are you ready？”and then call them after getting a reply. Of course I like to be asked too.

I would contact the italki teacher to set up a time.

I think the teacher should call, but I agree with Elena that it doesn't really matter. I'm always ready to call my student first, but if a student wants to call me, that's okay, too.