You can actually use "once after" in certain circumstances. In that sentence, "once after" is unnecessary but you may have instances where once after can help making a point on the sequence of events.

You need to use either "once" or "after", like this - Once they have left, be sure to stay where you are - After they have left, be sure to stay where you are These two sentences have the same meaning

No, but you may say either "Once they have left..." or "After they have left..."