To tame your own Pyromane, kite it to a body of water so that it acquires the Doused debuff. Continue to attack it to bring its health down to below 50%. Once sufficiently weakened, you should be able to interact with it to mount it. Once mounted, attack nearby creatures to apply a burning effect, then use Flame Absorb (ctrl-secondary) to absorb the flame to progress the taming meter. On Scorched Earth, Pyromane spawn in the wyvern trench, around which are no bodies of water. However, a wyvern is capable of carrying a Pyromane, so you'll need to pick up your target and drop it in the nearest body of water (for example, around the Red or Blue Obelisk) to tame them.

Passive: You need to tame it while the Pyromane is awake.