First of all, are you parking and drafting? If you do that, then there will be no untwisting. Spin the spindle, park it between your legs, draft the fiber, then let the twist into the fiber a few inches at a time until the twist weakens and you need to spin again. Repeat until you're really comfortable drafting and are ready to let the spindle hang and spin -- but keep in mind that that might not happen, and it won't necessarily be your fault. (My kit spindle will only keep spinning if I spin silk hankies on it. To this day.)
To keep the yarn from doubling back on itself, you need to hold it taut and wind it on with some gentle tension. If you pull it tight the yarn shouldn't break -- if it does, there's not enough twist in it. Doubling back is normal -- there's a lot of twist in the yarn and plying or resting will release some of that. Singles are twisty, especially the first ones you ever spin!