How does Homepod determine what music to play?

My question is a bit vague, deliberately. Here's my scenario:

Apple Music subscription member.

Large-ish music collection that was in iTunes Match before Apple Music launched (and of course, still is.)

One Apple Homepod.

iPad, iPhone and older Mac, but none of them are playing any music and not using airplay.

I have been able to play my music library with the Homepod, by virtue of the Match (and now Apple Music) subscription. I can also play anything from the Apple library. I can do this by issuing voice commands to the Homepod, or using Airplay from one of my hardware devices.

So far, so good. Now my question:

I power-cycled the Homepod while doing some unrelated electric wiring work around the house. When it powered up, my wife tapped the top, and it started playing my library, apparently via Apple's servers (aka 'the cloud').

Is this the default tap-on behavior of a Homepod in this scenario? Am I overthinking it, and should just enjoy the tunes? :-)

Thanks,

Tom