Thanks to that glory of the internet, baseball-reference.com, I've found out that the last 19 year old position player to be called to the majors was none other than....He does turn 20 in about 3 weeks. Last 19 year old position guy I can think of getting called up was Andruw Jones....
who was called up on August 4, 2004. This was 17 days shy of his 20th birthday.
King Felix was the last player to debut at 19, in 2005.