This depends mostly on what it is you mean by "DMPC"
Properly speaking, any character played by the DM is an NPC, a non-player character. Even major or regularly recurring NPCs like the PC adversaries and their lieutenants.
A DMPC is a derogatory (to my ears anyway) term for an NPC that is not only prominent and regularly recurring, but also in whom the DM has emotionally invested, in the same way that the players invest in their PCs, and who is generally on par with the PCs in terms of narrative and story focus. Often, but not always, the GMPC is part of the adventuring party, in the thick of things and generally acting just like a Player Character (not just a character) except run by the DM.
Having any DMPC (or GMPC to be generic and move away from D&D centric terminology) is almost always a bad idea, because it's a big conflict of interest-- the GM is supposed to be running the game for the players about their characters; if the DM is running a character in that sense as well, it gets very hard to maintain any kind of healthy objectivity.
But it's not obvious to me from your description that you are actually planning a GMPC. Mostly because you describe this character as acting, and supporting the characters, from the background-- most DMPCs of my experience are not backgrounders, but very much in the foreground. It sounds to me more like you're describing a prominent and manipulative NPC.
This doesn't mean you're perfectly in the clear, though:
If your inner DM voice is worried about having a DMPC, then maybe you do have that subtle, hard-to-quantify emotional investment in this character that could make it a problem
And even if you aren't emotionally invested in the character, you might be investing a little too much in the overall storyline this character represents.
Ultimately, Only You Are Qualified To Make This Call
Well, after the fact, your players will have a very informed opinion, too. But right now, it's on you.
However, I've found the following questions very helpful when assessing whether I'm accidentally putting a DMPC in one of my games:
What will I do if the players reject this character in some way? If that's going to cause anything in the neighborhood of bitterness or resentment on my part, then I have a problem.
What am I willing to do to keep this character on the plot lines I have imagined? The more willing I am to use the unlimited powers of the DM to force things back on track, the bigger a problem I'm creating for myself.