@Headlands There are no separate volume levels to set, but you have options for workarounds.
First, you can make an alarm for gym time that only vibrates. Actually, the Samsung vibration is pretty loud for a vibration.
Second, you can have the alarm be any .wav file you want. Record a quiet one and see if that works.
Also, you may be noticing increasing volume level on the alarm. This is a check box in alarm settings.
Bottom line is, you have so much granular control over alarms in xDrip+ that you should find something that works.
Edit: I reread your post and see that phone volume is pushed up when the alarm sounds. This would be an easy fix using Tasker. Are you familiar with Tasker?