When I am working on a piece of music, at the end of each work session, I delete the old version from my iTunes library and add the newest. That way I can listen to it on any of my devices, and see what needs adding, changing, removing next time I am working on it.
I have apple devices using IOS 5,6,7 & 8 and all can use iTunes Match. All except the IOS7 device, my iPhone4 can be updated as soon as the iTunes Match process has completed on my MacBook Pro.
Whilst the deletion is updated promptly on the iPhone, the new version appearing, and the ability to download it, can take anything from seconds to days. The only way I had found to cause the iPhone to check for updates was to sign out of iTunes Match on the iPhone, wait for the music library to clear itself of all but currently downloaded songs, then re-login to iTunes Match and have it download all the artist, album and song data from the rest of my music library all over again, before downloading the song I wanted.
Today I found I could cause the iPhone to check for updates when I wanted it to, by simply choosing Store/Update iTunes Match on my MacBook Pro, even though nothing had changed. Within seconds of that process completing, the iPhone was displaying the spinner next to the WiFi icon and the track appeared on the list to be downloaded. I tried it again twice and each time it did the same. It would seem that a signal is sent to all your devices to check for updates when the “master” library has performed an update.