Backman was handed a two-game suspension, one of which he served on Thursday night and the second will be served on Friday night.
Valdespin was issued a three-game suspension by the league, which he will serve through Las Vegas' game on Saturday.
On Monday night in Las Vegas, Valdespin hit a three-run home run in the second game of a doubleheader against the Sacramento River Cats.
Valdespin watched his home run, and carried his bat halfway down the first base line, before dropping it and rounding the bases.
Later in the game, River Cats pitcher Brian Gordon threw inside at Valdespin, hitting him in the hand. Gordon was issued a warning by home plate umpire Greg Stanzak. In the top of the next inning, Rodriguez threw at Sacramento’s Grant Green, hitting him. He and Rodriguez exchanged words as Green walked up the first base line, which triggered the benches to clear.
After pushing and shoving between Valdespin, Rodriguez, their teammates and the River Cats — and a lengthy screaming match between Backman and River Cats manager Steve Scarsone — they were ejected from the game.
Rodriguez was also issued a three-game suspension, but was optioned to Double-A, and will serve his suspension with the Binghamton Mets. Two players from the River Cats were also suspended.