How do we know if the managed service does its work on a monthly basis?

If you have doubts that you are doing your job, it is most likely that they are do not Doing your job You should not have to ask yourself if they are doing their job. They should tell you everything they do without you having to guess or even ask.

Everyone has their own way of doing things, but at least it should be fairly standard to tell them what is happening if they are administering it. If they do not, just ask them what they have done and what they are supposed to do.

You can always check the records to make sure they tell the truth, but if you feel you need to verify that they are telling you the truth, that is a completely different problem that you have.