Good question. You'd better contact the support team to make sure.

Italki has correctly managed the switch to DST and back again for me for the past five years. You just have to make sure you set the correct time zone in your settings.

I'm sure what your issue was, but I would guess it was because you tried to adjust for the time change when iTalki's scheduling system had already done so automatically. I've had classes today with students in two different European countries, and there were no issues with scheduling after my time had changed overnight. In fact, I've never had any issues with scheduling with students anywhere around the globe as long as the students have let iTalki handle the scheduling. The only times problems have ever arisen has been when students mistakenly thought that they had to make time adjustments on their own. If you let iTalki handle the issues with time zones and time changes, the system works flawlessly. It will always show you your lesson times in your local time zone already adjusted for any time changes.