Here are my thoughts about rust in a new barrel. I had that problem with a bore that was rough from machine marks both lands & groves. I used the old standard 0000 steel wool to smooth it out and experienced rust just like the OP. What I found out was it was steel wool particles trapped in the machine marks that was rusting not the barrel steel.
I finally switched from steel wool to fine valve grinding compound on tight patches to polish the bore, once the machine marks were gone and the bore smooth & shiny the rusting stopped.
Ballistol smells so good, I am not allowed to use it in the house so it lives in the detached garage.