Spetsnaz vs. Huntsmen

(Disclaimer: I don't own RWBY or R6S.) After Cardin revealed Jaune's transcripts, lying about him being the one to kill the Ursa, almost all the school hating his guts (minus his friends and girlfriend, Yang), being disowned by his father, and beating Jaune to a near death situation, Jaune finds his way to Earth, landing himself in Russia where he is sent to the Spetsnaz Training Faucility. Over the course of five years, he earns a name for himself by the callsign Fuze and is considered one of the five best Spetsnaz Operators. However, while serving with Project Rainbow, what happens when a the world of Earth is introduced to several teams from Remnant show up on earth through the same machine that brought Jaune here?