May was drafted by the Philadelphia Phillies in the fourth round in 2008, from high school in Kelso, Washington. The Twins acquired him in the December 2012 Ben Revere trade. He posted a 4.51 ERA with a 159/67 K/BB in 152 innings for Double-A New Britain in 2013, which was very similar to what he was doing in the Phillies system.
He's improved a great deal in 2014, posting a 2.93 ERA in 17 starts for the Rochester Red Wings in the Triple-A International League, with a 91/37 K/BB ratio in 95 innings with 75 hits allowed. The improvement in his command has lowered his FIP from 3.91 last year to 3.16 this season, indicating that the better performance is not just a matter of simple luck.
Scouting reports back up the numbers: he's always had a good fastball at 92-95 MPH, but he didn't locate it well and his secondary pitches (curve, slider, very good change-up) would come and go. Everything has been sharper this year, with more consistent command of both the heat and off-setting offerings. He's doing a much better job locating his pitches to all quadrants of the strike zone.
The main glitch this year has been a strained calf muscle that put him on the disabled list in June, costing him a month of action, but he's looked normal since coming back. He's averaged 145 innings over the last four seasons without ill effect; if anything his stuff has gotten better, helping him project as a durable starter.
May's walk rate is still somewhat high and some command wobbles should be anticipated, but overall he has taken a large step forward this season and doesn't have much left to learn in Triple-A. He is ready for a full major league trial. For his debut, watch particularly to see how he commands the fastball, and see if major league hitters can track his breaking pitches.