What I've been taught at several Smaart classes, is that both time and phase need to be correct for optimal phase-traces-overlay, between sub and main.
At the lower left hand corner of Dual's snip from merlijn, an example of 100Hz half cycles is shown.
If time alignment is correct / relative to 0 cycles offset, then phase can dialed in to find overlay without further consideration of time. All-pass can be used to bring whichever side, sub, or main, has the lesser phase rotation, up to the rotation of the greater side.
If time alignment is in fact relative to any of the half-cycles, it will be off by the implied time offset. Phase can still be manipulated to overlay even with the fixed time being off, but it will not be possible to achieve overlay for as wide a frequency range or as precise, as when adjusting phase with 0 time offset.
Pragmatically, whenever I'm convinced I've dialed in a good phase alignment, I reduce the fixed delay increment another half-cycles worth of time, invert the polarity from wherever it was at, and see if phase alignment can be further improved. If phase gets worse, I was at t=0 before already , so best previous alignment gets verified.
But the big thing / big problem for me...is it's simply damn hard to get good sub / low freq measurements indoors.
Reflections swamp the measurements. Must admit, I'm super skeptical of most all the indoor measurements I see posted of subs or mains down low, made indoors.
Anyway, I like to measure a sub out on the driveway, and lock in a phase trace and an acoustic distance, relative to the sub's front grill.
And do the same thing for the main, or better yet, time and phase align the whole thing stacked on the driveway.
Then indoors, either stack them the same way, or use a laser distance finder to front grilles, to determine what delays need to be put in place to make them arrive together, as if stacked on driveway. Indoor time and phase alignment is a bitch!!! .....

Lol