While this is not the answer you're lookin for, general info -
A quick .pdf search of AWS D1.1, D1.6 and ASME IX shows no mention of magnetism. Not surprising as I don't recall ever seeing weld code restrictions on this.
However, I would not be surprised to see restrictions in various company's internal specs due to previous issues with specific product lines.
Perhaps there should be mention in national codes as residual magnetism definitely causes weld issues, but that would wind up causing undue and expensive additional testing that would hinder production activities.
The only time I recall having to deal with residual magnetism specifications is print notes from the Design Engineer on some specific armor steel weldments for military purposes.
Your particular case sounds like is in need of a thorough root cause analysis and resulting internal specification restriction.
Tim