Sounds like a way to blow a fuse, if you had more than two test leads connected while measuring voltage with A and V connectors.. Now without intact fuse, negative path from charger to battery is broken, so anything connected to A is just same as if it is not connected at all.
Now, with broken fuse, if you have everything connected like in your diagram with my additions, charger wont “see” battery at all and may refuse to show any voltage. In that case, if you change test leads between A and V (what you are not supposed to do), you probably see some voltage, but it depends on charger what you will actually get.. If you got “proper” voltage that way, i’m pretty sure there is something wrong, as i would expect close to zero or few volts when charger is on and negative battery voltage when charger is off (or thinking that there is no battery)..
Even as electrician, i don’t like to measure current with multimeters.. It is so easy to screw up and blow a fuse. And with two channels in one device, you have to be even more careful. And then there are idiots like me, who tell other people to check their fuse a bit wrong, which does not help :D .. At least i should have said that you cant have anything else connected while doing it.