I've got mine wired up: MB Fusion Tuner out > Tuner In (back). Therefore the tuner mute isn't effective. I'll use the mute button on the amp when i want to tune. But that way I can put the tuner in standby and only switch it on when I want to tune up. It won't affect the signal because of the way I'm using it. Not ideal because I have to press 2 buttons to tune up (one to mute the amp, and then to switch the tuner on). It would be better if the MB Fusion had a mute footswitch, but I really don't think it's too much hasle.
The alternative would have been to plug my bass into the tuner and the output (from the tuner) into the amp at the front. Then the tuner mute would be effective. But it wouldn't have been as neat. And I don't know whether the signal continues to the amp if you put the tuner in standyby - I'll check next time I'm using it.
I also havent investigated whether I can plug the output from the tuner into the amp at the back - I don't think so, but any advice gratefully received.