You haven't done anythng wrong, you just haven't joined yet. The video probably used a longtail cast on, so don't worry about having the tails on two different ends. Put the needle tip with the last cast on stitch (it has the yarn that's attached to the skein) in your right hand, place a stitch marker on that needle and proceed to knit the first round. You may want to tighten the first few stitches to make sure there's not a lot of slace between your last cast on. Then when you get to the marker, slip it to the right needle and knit the second round. Keep going for two inches.
You'll be fine.