Ground loop current for voltmeter
Let's call your voltmeter and its 12 VDC power supply together as "The Meter".

Let's call the circuitry under your voltage measurements as "The Circuit".

You have no problems as long as the only wires or other conductive ways between "The Meter" and "The Circuit" are your two measuring cords.

If some third wire exists, you're in a trouble. The worst scenario: As soon as you connect your measuring cords or one of them, a short circuit happens.

Note: The third wire can be the protective ground of the mains AC outlet. You will do much better, if your 12VDC power supply in "The meter" is well isolated and do not need the protective ground for safety.