Advice for rebate on wrong water meter readings

Hi,
I’m after some advice and thought this was the best place to come.
Long story short but after a few phone calls yesterday we found out that our water meter has been mixed up with our neighbour and have been charged for their water and they ours. (We are only 2 people compared to their family of 4).
This could has probably been going on since before we moved in 4+ years ago.

I’m expecting they will contact me to offer a rebate but my questions are:
1. Can I expect it to be backdated to when we moved in?
Also as we have not used as much water as previously thought, not had so much water gone as waste. (down the plug hole etc)
2. Can we expect a rebate on the waste water as well?

Thanks in advance
Michael