The kitchen and bathroom faucets should not drip when turned off, however the shower head may continue to release water in the hose after you turn off the shower. That shower head dripping is normal and is not a defect.
However, in all cases, it’s a smart practice to turn off the pump whenever you’re not using the fresh water system. In the event you did have a leak, having the pump turned off would prevent you returning to your RV and discovering a major surprise.