Ullman was raised in the Conservative and Orthodox denominations of Judaism.
His family is Jewish, and his maternal grandfather, Joseph Ehrenkranz, is an Orthodox rabbi.
Ullman is best known for his starring role as Phil Diffy, a teen from the year 2121 on Disney Channel's Phil of the Future, a series that debuted June 2004.
He also starred as Roscoe in Disney's made-for-television film Pixel Perfect and as Sam in ABC Family's television film Searching for David's Heart (2005).
Other productions he worked on include Peter Pan at the Polka Dot Playhouse, The Music Man with the New England Repertory Company, and Just People at the Long Wharf Theatre.
He received a 1998–1999 Best Actor nomination from the Connecticut Critics' Awards for his character Stanley in Stamford Theater Work's A Rosen by Any Other Name.
While Ullman previously went by the stage name Ricky, he started using his real name in 2006 when he guest-starred on an episode of House In 2008, he appeared in an episode of the television series The Middleman.