I don't pre-starch my fabrics before using the strip cutter but I always don't pre-wash, so the fabric does have a little body to it when I run it through.
With the strip cutters, I have learned to stop about one-third of the way through to lift up the mat and pull the fabric straight. I do this again about two-thirds of the way through. Most of my fabrics are cut cross-grain, so I think the roller stretches the fabric as it goes through. Anyway, if I don't do this I find creases "ironed" into my strips and I don't like that. As long as I do the straightening, they come out perfectly!