I have not seen any rules that use them.
However, in theory the ref would step in the following situations IIRC....
1. Gladiator's get locked up for too long grappling
2. After a wound is scored, and then the Gladiator's could reset
3. Declare a winner
4. Enforce resets or penalties for cheating- Throwing sand etc.
5. Force a reset for broken or lost equipment
If I was going to place a ref in a game, some matches could be refereed. The Ref would need to move within three inches/two hexes/some unit of distance of at least one combatant at anytime, with the Gladiator with the lower "rating" being able to control the position and movement of the ref.
Games with the ref would do the following:
1. Potentially decrease the "Threat" rating for Mercy/Missio rolls and allow resets back to center in certain situations
2. Allow resets if a competitor was knocked down, lost equipment, wounded, etc. back to center starting positions
3. The Ref would also block Line-of-Sight, movement, or take-up squares that a Gladiator can not then use
Those are just some random thoughts on how to use a Ref model.