It appears to be like this for the vast majority of players. I believe it was originally planned for armor permutations to be updated on Bungie.net automatically, but because of how often people change their armor, colors, etc., it was causing server issues and had to be halted. There still doesn't appear to be much sense in whether certain players have updated armor on their profile or not (some just do, some don't, and how long they've been playing the game doesn't seem to affect it), and I haven't heard anything about it recently, so I'm not sure if they're still working on a way to fix this or not.
I honestly still think it'd be a good idea to simply give players the option to update their Bungie.net armor once a week or something. If we can continue to update player emblems so often, I don't see why one couldn't get their armor on here correctly at least once in a while.