That is the correct way of stringing. One half to one full wrap on the post. On the unwound strings, if you leave a little slack in the string - a LITTLE - you can get an extra wrap. I only ever seem to have a problem on the high E with some slippping.
Lots of wraps on the post is bad. The more string you have there, the more you're strings are going to have to "settle in" and stretch before holding tune. Then whammy and bends are going to be an issue - especially whammy where you push down, because the wraps will loosen, then you're in the same boat all over again.
On the wound strings, the key to not slipping is pulling the string TIGHT across itself when you make the locking "bend". A lazy bend at that point will let it get undone or slip. A sharp bend, held tight while you wind up the string presents no problem.
The method I use, is to line up the string hole in the tuner with the direction of the strings on the fretboard. Pass the string thru, pull it sharp towards the right (or left on G, B and E on a 3x3 tuner guitar). Pass it under the string entering the tuner hole, then pull it up sharp (make that crease in it) and bend it over. Then just wind up. It actually uses a bit less string than what was shown in the video, but takes a little more effort, as you have to line up the tuner holes with the direction of the strings - not really a big deal.
