Unlike Spotify, there is no app for Apple Music that lets you simply choose a speaker or Music group. You have to voice command it to start.
After you make an Everywhere group on the Alexa app of your devices:
Say "Alexa, play Apple Music, (playlist name) Playlist on Everywhere group."
Having said that, I find sometimes you should say “Alexa, play Apple Music, (playlist name), Everywhere”
Alternatively, you may need to say “Alexa, play (playlist name), Everywhere”
Some of this depends on if you have set up Apple Music as your default music or not or some other mystery I have not solved…
This is an Alexa problem as, Spotify is just as bad. But at least with that service, you can go to the Spotify app and just pick what you want and choose your Alexa group or speaker and be done with it.
Apple just needs to build access to customers Alexa speakers into the Music app and iTunes.