I wouldn't worry too much about the battery power level dropping immediately... that just means it is not at "full" charge. When you think about it, it makes sense. With a fully charged battery, just turning on one light will quickly bring the battery under full charge, even if a little bit. When we dry camp, the battery "drops" to 2/3 charge on the first night, but then stays there for 2-3 days under normal dry camping use.
With more dry camping experience, you will learn how long your particular electrical system will last on battery.