Well he was not appreciated in Stuttgart. The fans were after him, and even his coach at the time Zorniger made disrespectful comments following a Timo Werner goal celebration. So in the end I think it was easy enough for him to leave Stuttgart.
In addition to that Leipzig is known as a club with a good treatment of younger players. They have a policy of buying only young players and their team is in general very young. Not to forget is that the master mind of Leipzig is Ralf Rangnick, who in fact comes from the same small village near Stuttgart as Timo Werner (Backnang). Rangnick was a manager himself in Stuttgart and Schalke, but has now moved upstairs and is defining the whole operation of all the Red Bull clubs. He makes it very attractive to be in Leipzig.
Anyways as I said this is all just my opinion. You may be right that Timo Werner is just waiting for an offer from a bigger club.