Is this normal?

normal for tubes ... sure.
We all know how tubes are microphonic. This is a sort-of similar mechanism, but where the tubes' plates are actually physically vibrating along with the music. You don't notice it of course when the indoor speakers are on because their SPL swamps out those tiny vibrations which you're hearing.

Congradulations! You got a heck of a deal on amp with its own built in speakers :) Try Herbies Halo tube dampeners. It should improve the sound and get rid of the microphonics that's causing your problem.

You could blow your tubes with that kind of capacitance. The electricity is not able to get out of the tube essentially because it can't overcome the reach of the wire effectively. It's only a matter of time.