While this works around the current issue, it doesn't resolve the overall bug.  In reality, this is a couple of unrelated issues that manifest into one bug.  I would remove the code you added and do the following instead.
1. `Clock.prototype.tick` should check for `shouldAnimate` earlier than it's doing now, and only change any of the values if `shouldAnimate` is true.  Since line 986 sets `shouldAnimate` to false, the new code you added shouldn't be needed.  Make sure you add a new spec to to ClockSpec.js to account for the change in behavior.
2. `playRealtimeViewModel` in `AnimationViewModel` needs to have it's toggle function updated so that it returns false if `shouldAnimate` is also false.  Make sure you add a new spec to to AnimationViewModelSpec.js to account for the change in behavior.
3. Also, while it's not in the scope of the bug, I noticed that we no longer need a `secondsToTick` parameter in `Clock.prototype.tick`.  It would be great if you could remove this parameter, the two lines of code using it, and the two specs for it in `ClockSpec.js`.

If anything is unclear, just ask.