My guess is no extension. The max deal for the following season is what he must do. Home town discount for a lottery team? The kid deserves the jackpot, he's earned it. The comfort for those who want to keep him? Ainge can pay him more than anyone.
Why would he sign a extension/discount for Ainge? Ainge could ship him out the next day. His agent wouldn't allow it.
It's not a hometown discount. He signs an extension at a discount from what he would get as a free agent, because he gets the security of having a longterm deal in place before he takes the floor next year. It is insurance against injury or a regression (or lack of improvement) in his game.
If he doesn't sign an extension this summer, and comes out next year and gets injured, or doesn't perform well (and it is absolutely possible his numbers would take a big hit if they don't add some elite finishers around him), he would end up losing a lot of money.
It is always hard to tell how much of a gamble each player wants to take. But there are plenty of players who would take the extension now.