Italki shows you, the student, your own, local time for your lesson.
At the same time, it shows the same lesson to the teacher using the teacher's own, local time! Yes, your teacher often sees something different from what you see.
Nobody needs to worry about converting times. Italki does that for you. And it knows about time changes in countries that make them. You just use your own time to schedule lessons. Do not try to figure out in your head what time it is for your teacher.
Italki usually does this automatically. I don't know if Italki knows that daylight time is not observed in Arizona, though! If there's an issue, you can set your time zone manually in your Profile. Also, near the time it will show something like (UTC-05:00) which means that it is showing you UTC minus five hours. You can check somewhere--I use timeanddate.com--and verify that it's correct.