Summary
This past season was the first season that Vanderbilt has seen real NBA minutes, and he was able to show he could add some value. Vanderbilt hustles hard on the glass, particularly on the offensive end, and that's reflected in his rebounding rate being above average for a big, even while being undersized at 6'9". On offense, Vanderbilt lives in the paint as nearly all of his shot attempts come at the rim. If he can even become a reliable midrange shooter, that would make him more of a threat on offense. Even just developing a floater game would give him a weapon to use as the roll-man in pick-and-roll.

Vanderbilt is still only 22, so there's a reasonable expectation for improvement. I'm not sure Vanderbilt has shown he's worth more than a minimum contract, but I wouldn't be surprised if he got slightly more than that, and he has shown he's worth a guaranteed contract in my mind.
 
Cap Considerations
Vanderbilt will be a restricted free agent with a $2.1 million cap hold and Qualifying Offer, and the Timberwolves will have his Full Bird rights, meaning they would have no restrictions on re-signing him. If the Timberwolves don't think Vanderbilt is worth retaining for $2.1 million or more, they may not even tender him the QO, which would make him an unrestricted free agent.  

Other teams will have multiple ways to Vanderbilt as even teams without cap space could possibly use either of the Non-Taxpayer MLE, Taxpayer MLE, or possibly even the Room MLE to sign him to an offer sheet or outright as an unrestricted free agent. He also could likely be signed for the minimum.