Rags just use synced lyrics and if its lyrics only you have use the new lyrics song mode which gives you a length of time for your song and synced lyrics to get it absolutely perfect.
If you are running free willy than just adjust your time of song length to suit and auto scroll speed till you are happy.
You haven't mentioned how you run precisely so it is hard to help you as ST3 can run in so many different ways but i am sure you can get what you want by trying all options and finding the one that suits you, if ST3 cant do it no other software will, thats for sure.
Is this correct, you want to sing to lyrics at the beginning with lyrics then you want the auto scrolling to begin when you finished your intro?Do you have any audio backing?