The impression I have of the way the system works is:
You put your application in listing the school you are intending to train at.
The school you intend to train at receives a list of applications of students who intend to train at their school. Once they confrim your datails the TSA will ask for payment.
Once payment received preliminary approval granted and you will be asked for fingerprints. Once your fingerprints are received you should receive approval to start training (subject to passport photocopies etc)
Ensure your flight school gives you the correct information, I know of one that didn't ensure the information was correct for dates of study etc.