Interaction between Nivmagus Elemental and Rune Snag
You are correct, Player T should not have had to pay 2 mana.

The decision of whether or not to pay 2 mana happens as part of Rune Snag resolving. Player G has 2 options:

1) Let Rune Snag resolve, in which case Player T needs to pay 2 mana (or have their spell countered), but Nivmagus Elemental won't do anything, as Rune Snag will no longer be a valid target for the ability.

2) Activate Nivmagus Elemental's ability while Rune Snag is on the stack, exiling Rune Snag. Player T will not have to pay 2 mana, because Rune Snag will never resolve.

Note that option 1 will happen by default if player G does not specify otherwise. Player G has the right to respond to their own spell:


  116.3c If a player has priority when they cast a spell, activate an ability, or take a special action, that player receives priority afterward.


However, they must specifically state that they wish to retain priority:

(From the tournament rules):


  Whenever a player adds an object to the stack, they are assumed to be passing priority unless they explicitly announce that they intend to retain it.


So if player G casts Rune Snag without saying anything, player T can simply say "ok" or "resolves" or "I'll pay the mana", and it will be too late for player G to use Ninmagus.

This rule matters especially for Ninmagus in general; the player will always need to declare that they wish to retain priority if they want to ensure that they can use it.