Hallion was the plate umpire and crew chief during a game Sunday at Chicago against the White Sox and Price thought he missed a pitch. They exchanged words and the AL Cy Young winner accused Hallion of directing an expletive at him.
Hallion called Price a "liar" after the game.
Price, Hellickson and Moore later made comments about Hallion on Twitter. The pitchers were fined for violating MLB's social media policy that forbids "displaying or transmitting content that questions the impartiality of or otherwise denigrates a major league umpire."
The Rays were playing at Kansas City on Thursday.