Tabroom accounts and NSDA accounts are separate, And they each need to be linked separately to the roster on Tabroom or the NSDA. The only real connection is that I think Tabroom is set up so that if you try logging in with a valid NSDA account, it will accept your password and create a Tabroom account for you.
You can't do anything re: Tabroom on the NSDA site - everything related to tournament signups happens at tabroom.com.
The student needs to log in on Tabroom, either with a new Tabroom account they create, or, if it works for them, an NSDA login. They then need to request linking to a student on the Tabroom school roster in order for them to be able to do self sign-ups.
That is, they need to complete this process, on Tabroom:
...regardless of how their Tabroom account was created.