You ever hear a show where the DJ sounds great in the headphones, and then when the music starts playing, you can barely hear it? So you turn the volume up. And then when the DJ comes back on, it sounds like they are screaming at you?
In most MP3/MP4 based music files, even when streamed, there is an ID3 Tag that has the preferred volume of the track. While this is normally loud enough to hear, it isn't the same volume as a broadcaster's voice when listening to them on StationHead.
It is possible there is a setting on your iPhone/iPad that is lowering the volume of the music.
I have found that if you go into SETTINGS > MUSIC > SOUND CHECK = OFF, this helps alleviate the issue.
This also may explain the StationHead issue with listening using CarPlay as well. Although I haven't been able to confirm or deny this, yet.