Sync music library after setting up Apple Match?

I have had problems syncing my music library between my mac and my iphone/ipad (see Cannot sync iphone with mac, complaining … - Apple Community which did not offer any solution). Following one of the advices, I subscribed to Apple Match service.

After having set up the Apple Music program (on my Mac) took a long time updating the music library (which I expected; the music library on my Mac is around 100GB). After around two days' of signalling doing the update, and a reboot of my machine, the Music program does not signal any new activity; I presume this means that the Match service has been properly set up.

However... I do not see the results on my iPhone. I am looking for some private music files that I added to the music library on my Mac using the Music app; I expected to see that on the iphone's Music App as well. To no avail, it is not there. Nor is it on my iPad. Do I have to do something for kicking a sync on the iPhone side and download (or give access) to those music files?

In the (good) old days, I synced my iPhone/iPad with my Mac using a wire and that did the trick. See the problem I had above, and this does not work anymore. I thought Match will do it now; if it does not either, what do I get with the yearly subscription?