It sounds like the welders could have been qualified to AWS D1.6 or ASME Section IX. Both standards allow the welder to use either stainless or carbon steel test plates with austenitic stainless filler metal. One would have to review the requirements to see when it is permitted to use "substitute" (different base metals) for the test coupons.
In the case of GMAW, GTAW, FCAW, or SAW, the filler metals are all categorized as F6, so no harm, no foul. As I mentioned, it may be permitted to substitute different base metal for the coupons to save on the cost of materials for qualifying the welders.
With regards to FCAW, there are two families of FCAW electrode, those that require a shielding gas and the other that are self shielded, i.e., no shielding gas required.
So far, you haven't mentioned the governing fabrication or welding standard, so to comment on the visual acceptance criteria is like shooting yourself in the foot and wondering why blood is flowing from the shoe. While one would like to see a weld free of undercut, it may be permitted depending on the welding standard cited by the project specifications or purchase order. One can only reject attributes if there is acceptance criteria that addresses that particular discontinuity. A couple of examples: ASME Section VIII includes no visual criteria for undercut (the last time I looked), so how does one reject undercut if there is no acceptance criteria for it? Likewise, AWS D1.1 includes no visual criteria for several types of porosity, so how does one visually reject the weld for cluster porosity, isolated porosity, etc. when there is no criteria for that type of porosity?
Without the full details of the situation, it is difficult to say whether there is an issue with the welder performance test records. After all, if the welders have been welding without lapses longer than that permitted by the governing standard, their qualifications are valid unless there is a reason to question their validity. There is nothing saying the purchase order or project specification cannot require the welder to be qualified by testing for that particular job. There is nothing that says the "Owner" has to accept previous qualification. I typically require the welders to be qualified using a simple single pass fillet weld on a T-joint. It is fast and it sorts out the wannabes very quickly at minimal cost.
Just saying.
Best regards - Al