Interestingly, the "supervisor" I spoke to tried to tell me that the reason I was being charged interest in "arrears" or on a "back month" as she called it, was because when the statement is issued they don't know whether I've paid the previous month's bill in full. Of course this is nonsense. When I was issued my latest bill on August 19th, my balance from the July 19th statement was paid off on August 10th. The statement on August 19th includes transactions right up to the 18th.
I take some comfort in knowing that even AIB don't understand their own products.