Without getting too dull, when you have both a private pension(s) and the state pension they’re all taxable but there’s nothing setup to tax the state pension so they effectively add that amount to your other pension and tax it accordingly. Essentially you should be paying the correct amount just with someone other than the DWP dealing with the tax. It’s worth keeping an eye on it for a couple of years, just to make sure they’re getting it right.
I'm Autistic, if I say something you find offensive, please let me know, I can guarantee it was unintentional.
I'll try to give my honest opinion but am always open to learning.
Mark