I guess you'll get some more professional answers than mine but I'd say it's up to the look you want. Try it both ways. I'm knitting, for the first time, a big rag rug on Size 15s. It's strips of material and I didn't like it when it folded on itself because it didn't look as nice, so I slowed down and I put each strip around the needle flat.
It looks better that way. good luck! (I made a ribbon scarf that Ilove, that ladder stuff, but I knit English style)