Question: What happens when two players call the same tile for Mah Jongg?

Answer: When two players call the same tile for Mah Jongg, the player next in turn gets the tile. However, there is an exception to this rule. If two players call the same tile for Mah Jongg, and one of them has started to expose their tiles, they are entitled to the tile regardless of whether they are next to pick. 

Source: Mah Jongg Made Easy 2020 edition, pg. 20, # 13(b)