My team just gave up on Slack today, because push notifications seem too unreliable when we're on our phones. Paradoxically, we've found it works better when the app is not running than it does when it is running. Most of us are using Android phones. I couldn't find anyone else having the same problem, and I couldn't find any answers googling around, other than the obvious "turn on push notifications"-- push notices were definitely on.
We may go back to Slack at some point, if we can get it to work effectively for us.
The assumption is that if you're actively in the channel, you saw the item already and don't need a duplication notification on your phone for the item you just read.
To expand on this, the desktop clients keep you active for much longer than say the web client. I was also having these issues so I asked for a clarification from their support.
I stopped using the desktop client for this reason and now I have a separate window open for the web client. Push works much better for me now.
What the other reply said is true, Slack by default only sends mobile notifications when you're 'away.' In addition, by default, it waits 5 minutes before sending notifications (this can be changed).
The v2 Android app is currently in beta - I've been testing it for several weeks. It's lightyears ahead of the current release version which is admittedly pretty faulty (no caching means that resumes are very slow). I've also found notifications to be more reliable. Perhaps give it another try once they ship the v2 Android app.
We may go back to Slack at some point, if we can get it to work effectively for us.