I also have the EXACT SAME PROBLEM. I'm on an iphone SE (which is technically a 6s, but smaller) and when I use hyperlapse, it distorts the sound of the iphone during playback, and also distorts the sound of ANYTHING on the phone (ring tones, texts, other videos shot with stock app, and music).
It's a new glitch that just started appearing once I updated my phone, so I'm thinking it's a software glitch. But I'm hoping that either hyperlapse (i.e. Instagram's purchase of the LUMA technology responsible for the great stabilization) will figure out a fix. I'm guessing an update of the app may fix this, though my friend had the same issue and said this didn't help.
Any tips would be GREAT. I love hyperlapse but won't use it until this is fixed, as it renders my iphone pretty useless.