I think they do start..
If you made an action for them to start and your conditions are correct, they should..
But like I said, the timer starts "every tick" the animation is playing, so as long as the animation is playing the timer is restarted every tick, which will in effect only really start the timer the last tick the animation is playing..
If you could share your events, this could be easily checked..
The solution might be as simple as adding a trigger once condition to the event starting the timer..