Is this normal?

Wild guess, forgive me if I'm wrong. Perhaps the capacitance of the long run to the outdoor speaker is causing the tubes and / or transformer to resonate along with the music. Sound would be similar to putting your head near a phono cartridge with all the electronics cut off and hearing just the mechanics.

Perhaps there is a better answer, this is my best guess.

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.