@Gigi91
I think you are understanding the long term policy correctly, but you need to make a formal change on the site for your host to accept in order to avoid being charged for the last month. As the monthly price might be based on your length of stay, you might be asked to pay a higher rate.
Alternatively, make a cancellation in time to avoid the last instalment, but this is not likely to go well with the host and you risk a less than stellar review.
First and foremost, discuss the situation with the host so that you can make an agreement that will benefit both parties. The earlier you notify the better as this may allow the host to rerent. Loosing a month of income is not fun.