Blue tooth connecting to neighbor's speakers

I have Avantree headphones and a small transmitter that I thought would work for just within my apartment. Recently, a neighbour one apartment over, and one floor down, came to me and said that he figured it was my system connecting to his. I'm up early and they have been rudely awakened by my music coming through their speakers at 5:30 a.m. -- and their system wasn't even turned on! I do not know how this is possible. Until I get the new transmitter, they have to remember to unplug their speakers at night.

I have reset the transmitter and head phones according to Avantree instructions and I thought it had worked. But I got a text from the neighbour at 6:00 a.m. today that says otherwise!!!

Avantree said they'll send me a transmitter with less power, but I still don't understand how it can go through walls, floors, and glass to connect to speakers that aren't turned on!!!
An explanation for this would be very helpful. Thanks.