If it keeps rusting every time you wet it… stop wetting it.
[I'm not watching someone clean a pan for 17 minutes just to see exactly what they're doing. That it even takes 17 minutes to show me how you clean a pan gives some hint already that you're really overthinking something, somewhere.]
Get it dry as rapidly as you can by not only wiping it round with several paper towels, but get it on some heat as well.
Once it's dry, one last wipe round to get the last of it off, then start seasoning. That last little bit of staining is unimportant, it will just get buried in the seasoning.
