It sounds like, in your current setup, you are looking to make sure that the TextToSpeech behavior doesn't execute before the beginning of the animation and, currently, it is starting a moment too soon.
One of the best methods to sync up the beginning or part of a PlayAnimation behavior with a separate behavior like TextToSpeech is to use the event layer in the animation tool (described here) in conjunction with the StartOnAnimEvent decorator in the behavior tree.
In the behavior tree that would look like this:
That tells the TextToSpeech to wait until it gets an event from the animation before it executes. To make that work you will also need to add an event layer to your animation, key the frame that you want the TextToSpeech to wait for, and give the event the same Name property as you enter in the eventName argument for the StartOnAnimEvent decorator in the behavior tree. You'll see in the above screen that I set the eventName to "eventhappen".
In my skill, I wanted the TextToSpeech to wait until the 150th frame of my animation. So, I added an event layer to my animation, keyed the 150th frame, and placed "eventhappen"in the Name field as seen here:
For your purpose you might want to key the first frame of your animation with the event layer if your primary goal is to make sure that the TextToSpeech behavior starts at the same time as your animation.