Yes, the accurate way to record revenue is as the service is performed. But due dates are not a good proxy for services performed.

Tuition (or membership fees) should be coded to a deferred revenue account (a liability account) in full at the time of invoicing, and then moved gradually to revenue via GL journal entry as the the revenue is earned. It's the mirror image of prepaid expenses, such as insurance, which are gradually expensed via GL journal entry.

Adjusting due dates in AR should have no GL implications.