Clean it well of any oil's.
(oiling after rust browning is part of the process)
Then a paste of backing soda scrubbed in with a tooth brush,
Or even better Household Ammonia. Right out of the jug as is,, is best.
Rust browning is usually coating the barrel with an acid based solution to speed the rusting process. The opposite a "Base" solution is applied to stop the rust. If the base wasn't applied evenly or if they missed a spot it will continue to rust.
Hopefully you can treat the barrel out of the stock so as too not harm the stock finish. But either way ya gotta get the neutrilizing agent down into the bare metal, if any oil is present it will in affect protect the rust.