Sounds like you have it handled. Your insurance company does this every day and it is protection that you paid for with your premiums. You should definitely let your insurance company know if you get any further contact from the subrogation attorney. If at any time your insurance company refuses to defend you or says "sorry, you're on your own", then you have an issue but unless that happens, it sounds like they've got it covered.
Like others have said, subrogation is a real thing. Consider an accident like a two round boxing match. Round one, the initial accident litigation/settlements has been completed and you rightly thought this whole thing was behind you. But this is round two, the final round of this two round boxing match.
Subrogation is when the insurance company pays out according to their policy but believes it that another party is ultimately responsible so they go after that party to try to recoup some or all of what the insurance company paid out.
Lawyers have to eat so they generally only take cases when there is some meat on the bone for them. Usually, subrogation attorneys get a % of what they recover for the insurance company that paid out on the claim. Some subrogation claims are clear, some are murky, and insurance companies have all kinds of agreements as far has how to handle these things between themselves.
You're smart not to post anything about the facts on here but there can be instances where the rear car has 100% liability like if a car crashes into the car in front of them which pushes that car into the car in front of them, etc. Or there can be cases where the rear car has 0% liability like then the pile-up already happened and the rear car barely taps the last car and causes no damages. And there's the in-between where the rear car did not cause the initial accident but made it worse by hitting the rear car.
I mighta taken the long way around the barn on this one but, in the end, you were a responsible person and had insurance so they should handle it. It's what you paid for.