The only time a Style ever does anything is the moment you activate it. It will apply its settings to the lister. After that the Style has no effect and when you change folders all that matters are Folder Formats.
Unless, that is, you make the Style switch on the Format Lock, in which case its settings will be locked in place. I'm not sure how that applies to auto-sized columns, though. (The Format Lock may lock the column widths in place rather than the "auto-size" setting.)