Aw, so sorry to hear the poor thing was being mistreated. Good on you for rescuing it.
Just something to keep in mind. Welcome to the forums!
I'm not an expert, by any means, but...you may have to keep the idea of rehoming the tiel in the back of your mind. What if he doesn't get along with the budgies or the finches? You can't force him to live with other birds if he turns out not to get along with them, or you'll have fighting.
Just something to keep in mind. Welcome to the forums!