More in detail: you pay now for Aug 2021 - Jul 2022 with the old address you move in October a while after you move you receive a negative bill (= they owe you) for the period Oct 2021 - Jul 2022 and the old address; nothing to do or pay next year you'll receive a bill for Oct 2021 - Jul 2023 with the new address; the amount for Oct 2021 - Jul 2022 will compensate the negative bill you received after the move, the amount for Aug 2022 - Jul 2023 is the net amount you'll actually pay - the normal yearly amount
All this dance because they invoice per address/household. But you don't have to worry : you pay a yearly bill now, you'll pay another yearly bill same time next year. They will just send you a couple of letters reflecting their internal procedures, but mainly FYI.
I paid back in May, but it seems as if I may leave the country in the near future. Any inkling of whether they would refund something?