Hi Oksana,
I think one of the most interesting things about italki is that every teacher has their own way of doing things. Of course, this can be tough for new students as they might have expectations of what a lesson should be like, and it might take time to find a teacher who matches your style and expectations. As a teacher and a language student on italki, I would highly recommend you to message any potential tutor before-hand with any specifications, questions, doubts, or requests so they can take them into consideration. Of course, if you are looking for a professional tutor, their qualifications should be listed on their profile, but feel free to ask them about these in the trial lesson!
What I always do when looking for a new tutor is first, to message them with a message telling them as precisely as possible what I am looking for, and asking them if they feel comfortable in meeting my request. Then, I'd book a trial or single lesson and get a feel for the teacher. If I would like more activities of a certain type then I would directly tell the teacher ...if in the second class they don't meet my request, I wouldn't continue with them. If they can adapt to what I want to learn, then great! I would continue with them.
All in all, don't be afraid to communicate with potential tutors before your lessons! :)