You are not alone on this issue, I have had this issue even on the latest version of iTunes (12.3). Many are experiencing this. Apple released iTunes 12.2.1 back in mid July, which was supposed to address this problem, but it still persists for many, even with the latest updates.
For me, it has been a mess to have both iTunes Match and Apple Music because it is hit or miss. Some of my music will match and others are apple music format.
I would strongly encourage you to send your feedback to the Apple feedback page: apple.com/feedback/ and also voice the issue by opening an iTunes support ticket.
I had enough, so I downgraded to iTunes 12.1.2, the iTunes version just before Apple music was released.
Some things you should know before considering this option:
1. This version of iTunes does not have the Apple Music feature on the desktop iTunes (you can still continue to use Apple Music on iOS devices with 8.4 or later)
2. In order to downgrade iTunes properly, you will be required to use a third party application called Pacifier for the downgrade to work properly (I can link to a discussion thread on here if you signal interest to go this route)
3. If you downgrade, you will lose metadata because you will have to delete the itl file stored in your music folder. So play counts, star ratings etc will not be up to date. If that matters to you, you should NOT downgrade.
If you have been backing up your computer, you may be able to retrieve the metadata file from an old backup, if you can remember when you updated from iTunes 12.1.2 to 12.2
It is a band aid fix, but that is what you will have to do for now until the issue is resolved
