When I do the fold over, the feathers need to be wet. This allows the vanes to be pushed back against the grain, so to speak, when you are tying down the end of the feathers. The wet feather also bends without cracking... very important.
The advantage of the "fold over" is the fact that you can pull the feather very tight when you are tying down the front part. This keeps the fletch close to the shaft. All the two-fletch feathers that I've seen on actual artifacts are never glued down to the shaft between the wrappings.
You need to let the sinew dry a bit before folding it over and pulling everything tight, though. Maybe 3 to 5 minutes. This allows the glue to "gel" and hold the sinew fast. If you need to wait a long time, because the sinew is taking forever to set, you might need to smear a little water on the part of the feather that is folding. This prevents cracking. Most feathers are pretty flexible, so this is not usually a problem.