Investopedia seems to agree with you; a back charge is:
A billing made to collect an expense incurred in a previous billing period. A back charge may be an adjustment due to an error, or it may be to collect an expense that was not billable until a later period due to timing issues.
The latter is what you're describing - a bill for something the month after it's really proper because the landlord doesn't know the right amount at the time of the initial bill (since rents are payable in advance, as opposed to mortgages which are payable in arrears).
I would say that personally I wouldn't find that term familiar in that context; while I knew what it meant in context, I think that if you're writing up a description for a rental agency or somesuch, I would either explain it like you did in the original question or use a more common term like "bill". In communications with more technical folks back charge seems right, though the real estate folks around here might be able to tell you if it's common in the industry if that's relevant to you.