Utility companies bill in "arrears". This means that you receive the bill after your actual usage dates.
For example: Imagine that your billing cycle is December 1 - December 31. The meter will be read on the 31st, and the bill will be generated after that. It may be several days before it is ready. SimpleBills then receives the bill and prepares your invoice. So, you would receive the bill in the following month.
If you moved out at the end of December, you could expect your bills to be received after that time!