Yeah, in missions and stuff it shows you putting it on and then jumping but doesn't show it when jumping in free-roam, which is a downer really. The cosmetics really do change the feel of the game.
After you get more into the game you'll get parachutes by getting into planes and choppers like the games predecessors.
I remember when I base jumped there was a quick clip of my character grabbing the chute and clipped it on. But normal jumping it just sort of appears as you've said.