I believe the reminder icon will automatically appear when your
opponent hasn't moved in two days, regardless of the time-out period
selected. When the icon appears, just click on it and a reminder is
sent and the icon then will disappear. If your opponent hasn't moved
and the time-out period is reached, another icon will appear allowing
you to claim a victory against that opponent. You do not have to send
reminders or claim victory. It is optional on your part.
Regards, Marc Miller