When I buy a song at the iTunes store, it usually will show up in MyMusic on that same device. But it _won't_ show up in MyMusic on any other device, even if those devices are ALSO using the same AppleID and are logged into iTunes and MyMusic using that AppleID (heck, even if they are both using the Match library). This is incredibly annoying. If you turn on automatic downloads for music, problem solved, but then you get everything. So. What to do?
Every other time, I've tried all kinds of crap trying to force a refresh. Generally speaking, if you bought a single and you went to look at the album listing that single is from, you can see on other devices that that track is "Purchased" -- but you can't get it to download from there.
Here is what DOES work:
Go to "More" in iTunes store, then Purchased, then whichever media, but for us it is always Music, then I always go to Recent Purchases, but you could find it via the band name or whatever. Recent Purchases takes a while to load -- you can tell that this is the one time that an actual database check occurs. Then there's a download cloud icon and you can download it.
If I bought on my son's phone, I won't need to do anything else on my own phone. But if I bought it on my phone, I'll need to enter my AppleID password in order to download it. Why? Why, Apple, why?
Things that DO NOT work: killing the instances of MyMusic and/or iTunes store in hopes that something will change when they start up again. Going to Recently Added in MyMusic to see if it is listed there. Searching by title or artist with Show All Music enabled (remember, in all these cases, it's on a shared iTunes Match library).
There are _so many things_ about this situation that don't make any sense to me (particularly WHY don't those things work on the MyMusic side? but also, why can't you download it from the Purchased indicator on the iTunes Store side when you are looking at the album listing and it shows one of the tracks as Purchased). R. says, this is so typical of Apple. I disagree. This is _very_ atypical of Apple. Apple software often fails to work in really odd and obscure ways. But this is a database interaction that is failing in a really obvious and irritating way (a couple, actually, if you count the part where I have to type in my password on my son's phone to download but not on my phone).
If you are still reading, and you've never had this happen and you are very confused, just don't. Go do something else with your valuable time. It's bad enough that Apple has destroyed my equanimity so many times. It shouldn't be wasting your time, too.