I don't know if this applies in your case, but after my lithium battery & inverter/charger upgrade I also added a battery monitor. When plugged in, my battery monitor shows there is a small current being pulled from the batteries. My understanding is this is due to an internal neutral bonding to pass through 120v current to my coach. (My brains not working well today, so this description is probably neither perfectly clear or correct).
Suffice it to say that you could be experiencing a small drain while plugged in. But, once your batteries deplete to a specified level, this drain should be offset as it should also initiate a charge cycle.
So if you don't have a reason to plug in, I'd just check the voltage once a week or so for phantom drains. Then charge when needed. But I think you'll be ok either way provided your charger is working properly.