If I select Minion Pro Italic, I get no swash option (the button is greyed out) and so I cannot use/toggle swash alternatives. If I select a font (like Garamond Pro Italic), I am able to choose swash alternatives. If I then switch to Minion Pro Italic after enabling swash, I see the Minion Pro swash alternatives being used, but the swash toggle is disabled.
To toggle swash for Minion Pro, switch to a font that supports swash, toggle swash, and switch back. (To merely disable it, pick any font that does not have swash support).
Photoshop probably just queries the file headers for font support when setting up the user interface for the font, and doesn't actually search for the existence of the glyphs (perfectly normal behavior). My guess is that the font does not enumerate the swash option, despite the presence of the glyphs.