Progress

I started off the text by taken what is spoken first. I arranged them into  a neat order by pulling guides from the ruler so when they appear they're not just placed in a random order.

I then used key frames to make them come in at the right time and in correspondence with the waveform.

Once i done that and had them coming in at the right time, i created a null layer and parented the text layers to it. So then i could control how the text came in, when a word appeared it would be centered, then move to make way for the other word coming in next. I also added motion blur just to give it a bit of effect :)