I live in the United States. My teacher lives in Spain. I want a lesson at 1 p.m. I make a request. On my screen, I make a request for a lesson at 1 p.m.
On her screen, my teacher sees a request for a lesson at 7 p.m. She agrees.
Now, we both see the appointment. I see it on my screen. She sees it on her screen.
When I look at my screen, italki says the lesson is at 1 p.m. (EDT).
When she looks at her screen, italki says the lesson is at 7 p.m. (CEST).
Everyone sees the lesson time in their own local time.