Same thing is happening with me from day one. I've got "Always On (Disable Sleep)" enabled/on and playing music on Spotify in the background. iOS 10 on an iPhone 6s Plus.
Weird example: I started stretching when there were two minutes left of the cool down according to the app (but had been at it for 34 minutes already). I locked the phone, continued stretching, then I heard the usual announcement when you finish a run. 20 minutes later, after shower, I unlock my phone and the app is counting down from about two minutes! Then when that finishes I hear the announcement again.
Some walk phases last for at least three minutes.
What on earth is going on. Is this a known issue? Is it being handled? I'd rather switch to another similar app than wait months for a fix or a workaround.