AF records (ie the AFORMS printout) don't distinguish between having the A-code or not. Therefore to be fair to everyone, SWA accepts ALL time coded as MP or IP or EP as PIC. Primary vs Secondary is of no concern. "Other" time is of no value, generally. (You could point to a flight and claim that you were PIC & A-code for the whole thing, even the part of it you were out of the seat... you might get them to buy into that, but it'd be an uphill fight in light of their statement about "NO 'other' time will be accepted." I figured that the A-code "Other" time balanced out the non-A-code MP time and left it at that.)
The point of the "primary time will only..." sentence is that primary time as a copilot, even though it is "hands on" and meets the FAA def of PIC, does NOT count for SWA purposes.
Once you've upgraded, Secondary is just as good as Primary since hands on or not, you're still the PIC and making the decisions.