Looks like he'd be eligible for it later, but his first max deal wouldn't change. What I found is that a player would be eligible for the bigger extension on their 2nd contract if they were traded during the first 4 years in the league but not after, which is why Cousins couldn't get it from New Orleans. This first max that he signs would be the same whether he signed it as a Sun or Wolves player, it's the 2nd that it becomes a question but it wouldn't matter in his case because if he was traded after 3 years in the league he'd be fine so long as he stayed with the team who traded for him throughout his first max deal up until he signed that new contract, which would be 4-5 years down the road. He may qualify for the Derrick Rose rule though, allowing a higher max coming off of his rookie deal, if he's able to hit the criteria this year. He has 1 All-Star appearance so far and no All-NBA team appearances but the awards haven't been named this season. I think he'd need to be an All-Star again or be named to an All-NBA team to be eligible for the 30% max coming off of his rookie deal.
Question 24 details the max...
http://www.cbafaq.com/salarycap.htm