I don't get if Volgin was working with Skull Face later on in the game or not? He sure was not at the beginning. Same for Mantis.
Mantis is drawn to the negative energy of others. That's why he forms a bond with Volgin when he is brought into proximity with Volgin's remains. Both are Soviet experiments.
At the beginning of the game, Mantis and Volgin are on their own. Mantis likes to bring two enemies into close contact, which is why he brings Volgin to the hospital, seeking out Big Boss, the subject of Volgin's angst. XOF get killed in the crossfire.
However, Mantis is what led Skull Face to the hospital in the first place.
From pg. 341 of the official Piggyback guide written in cooperation with KojiPro and Kojima himself:
"After a plane crash, in which The Third Child was the sole survivor, a chain of events led the boy's mind into sufficient proximity to sense Volgin's boundless enmity for Big Boss. With this, their association was forged: Volgin, a scorched carcass imbued with an overpowering obsession to kill the man who destroyed his dreams; and The Third Child, who could facilitate his desire for vengeance. This conjunction gave birth to the creature known as the Man on Fire."
"This was also, it transpires, the means by which Skull Face learned of Big Boss' location after a nine-year search. Having received word of their curious relationship through Cipher channels under his control, Skull Face took an interest in the case of the strange child and the former Soviet colonel.
This led to a momentous development. ... When Skull Face investigated the particulars of the plane crash, he discovered that the events that led to its destruction began over Cyprus: caused, Ocelot later posits, by The Third Child sensing the latent anger of Big Boss far below as his flight passed overhead. Skull Face thought this anomaly worthy of further scrutiny -- which led to his discovery of Big Boss."
Again, it's from the official guide. Kojima himself. Later on, after the hospital incident, Skull Face tracks down Mantis and the Man on Fire and asserts his own negativity over them, giving him control of Mantis and, by extension, Volgin.
Skull Face later loses control when Eli comes along. Eli's hate is so strong that it overpowers Skull Face.