I'll try to answer your questions wearing two hats here...(1) After 25 years in the restoration industry, I sort of understand the insurance side of it, and (2) I'm also an investor so I know where you're coming from.
Public adjusters are not legal in my state (Alabama), so they're really not a factor for us. Knowing what I know about the industry though, I personally would not hire one. It makes more sense to hire the GC that's rebuilding both the units next to you. He'll get the benefit of having three jobs in one place, and I'm guessing, combined, this would be a decent sized job for his company. That means there will be a lot of employees dedicated to making sure this runs smoothly. Can this GC also do any water mitigation that might be required, or will they tear this down to the slab and start over from ground-up? Right now, you really don't know until you hear back from the IA.
Your independent adjuster is currently writing an Xactimate estimate based on the repairs for your unit alone. The other two units have already filed with their own insurance carriers, so as of today, the liability part of this is not a factor. We will come back to it though.
If you choose to hire a contractor quickly, he should scope the loss and write a competing Xactimate estimate that can be presented to your adjuster. More than likely his estimate will be a LOT higher than the IA's estimate (at least it is when we write one), but that's OK...your contractor and the adjuster will negotiate back and forth until they come to an agreement. Just be sure to have an agreement IN WRITING with your contractor UPFRONT that states you won't be held responsible for anything more than your deductible, unless it's approved in writing by both parties (email is fine). Hopefully you've got good "code-upgrade" coverage in your policy, as this will become a factor if it's an older unit.
But before you sign with the contractor, verify with your neighbors that they actually have hired him to rebuild their units...Contractors will lie. Also, you'll want to vet the contractor every which way you can think of...Google reviews, BBB reviews, GlassDoor, Facebook could be a big help here, also look up any lawsuits they've been a part of in their county. Ask your adjuster if he's ever had any dealings with them. Most carriers won't let their adjusters say anything good or bad about a contractor, but this guy is an Independent...Tell him it's completely "off the record," and he may be a little more open about it. You can ask the contractor for references, but that's usually a waste of time. They're just going to send you to their happy homeowners. You'll never talk to someone that dislikes them...and if you've been a contractor for any length of time, there's somebody out there that dislikes you.
You mentioned liability because the fire started in your unit...what was the cause of origin? If the CO was cooking related or anything similar that's directly attributable to your tenant...that's when their liability kicks in. Hopefully your tenant has renters insurance. If so, the liability portion of their policy will kick in first, then yours will follow.
On a subrogation claim like this one seems to be, that's usually played out behind the scenes between the three carriers involved...and potentially four carriers if there's a renters policy. But either way, I wouldn't worry with that part yet. There's nothing you can do to change anything now. Everything is determined by what policies were in place the day the fire occurred. This sounds like it could reach several hundred thousand at least, so the other carrier's subrogation departments will dig deep on this one. If this was an electrical fire, there will be a lot of questions about what you replaced and when. Who did the work, what materials were used, etc...They're trying to find an angle they can subrogate to. Maybe it's an electrician that you hired six months ago that did something wrong, or maybe he used a certain model of a breaker that's known to fail....If there's an angle the carrier can use to collect their money back from someone else, they will usually go after it.
Pay attention and take lots of notes about everything going on. If you stay in the landlord business long enough, it will probably happen again at some point. Also....take LOTS of pictures along the way. You'll never know when one picture can save you $25k....it happens to us all the time. Good pictures can save your butt.
Good luck and I hope this goes smoothly for you. I'll try to keep an eye on this thread going forward too.