Do clients get appointment confirmations and reminders in their timezone?

Yes, appointment confirmations and reminders are sent in each client's specific timezone, as setup by the coach in CONTACTS TAB > CONTACT NAME > "Profile" tab > "Client Information" section. If it seems to you that the notifications are not sent according to the client's timezone, you need to make sure that their timezone setting is correct in the section mentioned above. It could also be that you are looking at the appointment notifications sent to you as coach, so in that case they have your timezone.