House Batteries Disconnect Switch & Inverter

When connected to shore power, the inverter screen shows an icon showing the power going from shore power to a light bulb, instead of coming from the batteries. The screen will appear for a short time, even if the inverter itself is turned off. I just want to make sure when I turn the battery disconnect switch to off and I turned off the inverter the batteries won't be drained. As I mentioned before, I've owned coaches before with inverters and never had the batteries die on me while in storage. I was a bit concerned this inverter may have been different than the previous ones I had.