I realised the first post is form 2013 but here is my answer anyway.
I have an iPhone 5c with iOS 8.4.1 software
If you disable the option 'Change with Buttons' on the volume menu, the volume for the ringer and alerts will be separate than the one for the alarm, which can be set with the side buttons.
Ringer and alerts (text tone, new voice mail, new mail, set mail, tweet, calendar alerts and so on)
Settings --> Sounds --> Ringer and alerts volume option: just slide it to the volume you want.
**Important, unable the 'change with buttons' options. When you do, the extra info text reads: 'the volume of the ringer and alerts will not be affected by the volume buttons'.
Alarm
Just adjust the volume to the level you want by using the side buttons. That's it.
Result
Ringer and alerts will sound at volume level set through Settings --> Sounds menu, regardless of the volume set through the side buttons.
(Morning wake up) Alam will go off at the volume set with the side buttons.
Tips
a) You can silence the in calls and alerts by using the 'silent' side slider. The alarm will still go off normally (and soundly).
b) By turing the silent side slider on and off you can check on your screen the volume the ringer is set up at.
I've tried all the above and it worked for me. Hope it works for you too.