All of these processes are based off of real life processes for artificial gemstone creation.
Flame fusion process
This process takes a powder, pumps oxygen and a gaseous fuel (hydrogen), and pushes the powder into a very hot flame, melting it. This melted powder then gets deposited on a ceramic pedestal to form a boule.
Translating to Trove's mechanics, this is a process that could be used to convert gem dust into actual gems. As it is powerful, it probably should require a soul from the shadow tower or gem sparks for crystal and above. Since you guys (the devs) are thinking of having mystic gems this can be a way to time gate their creation.
This process in real life requires no flux. This can be balanced by not having this method be able to level up gems. Also, the flame fusion process creates some very subpar gems, due to gas pockets, visible banding, and cracks forming when being polished.
Crystal pulling process
This process inserts a seed crystal into a molten mix of the gemstone's chemical compounds. This is the fastest method for gemstone growth, but it wastes a lot of gemstone materials. It is so fast that the entire semiconductor industry cannot exist without it. This method of upgrading gems can be done just by creating a crafting station. Not the gem forge, but a gem crucible. Personally, I'd rather decouple the ability to upgrade gems from the gem menu (because hourly challenges).