Don't overthink it; readers will generally go along with whatever terms you want to use, as long as you explain it sufficiently, and as long as they aren't wildly out of whack with their expectations.
As a reader, I know that each story may use terms in slightly different ways, or in ways that have different implications for the story you are telling; this is especially true for terms referring to magical/mythical/fantasy/sci-fi elements that frequentlyoften differ from fictional world to fictional world.
If I read a story about a character described as a "vampire", I don't know (yet) whether this means they wear a tuxedo with a cape and sleep in a coffin, whether they are part of a powerful ancient race of immortals in perpetual war with the werewolves, or whether they are just a brooding teenage goth.
Any of these (or something else entirely) are fine; I just need you, as the author, to explain to me what you mean by that term. Just don't call someone a vampire and then explain it's actually a little green man from Mars.
In your case, you should be totally fine using "pyromancy" and/or "necromancy", and simply clarifying what that means to the characters in your story. I don't think readers are going to even know the strict definition you're alluding to in this question (I frankly don't see the distinction you're trying to make), all you can assume is that readers will (probably) recognize the roots "pyro" and "necro"; the rest is up to you.
In the same way, though, if you have a story-related reason to use "pyromagus" and "necromagus" instead, I don't think readers will have a problem with that either. Perhaps if you had mage guilds that were all named based on their specialty, calling them "pyromagus" and "necromagus" (and aquamagus?) makes the most sense.