I'm pretty sure enemies can only see the circle for the actual jump, so they have 3 seconds to get out.
What I do, is I wait for someone to attack one of my allies, then ambush them.
For example, I was at my fountain. buying. I saw my teammate, MF, was headed for dragon. She gets there, and Taric is heading to mid, so he's already right next to dragon.
Our mid has a champ in it, so I knew he wouldn't retreat that way. So I put my drop on the little lane heading to purple's blue buff golem. Worst case scenario, he runs to bot lane, and starts running back to his base, in which case I'll be right there in the jungle ready to pop out and attack him.
Sure enough, Taric, after realizing he can't 1v1 MF, stuns her and ran towards his jungle. I drop right on top of him, stun him and MF gets the kill after catching up.
You just have to anticipate a little better.
Another thing I do with him is, if I'm in top lane, I'll go into one of my bushes along the edge of the map, I then ult to the bush next to mid lane.
Gank positioning without the MIA call from the other team.
Then obviously, if you and your team is pushing a lane, but there's a big minion wave on one of your towers, you drop on it, get a bunch of gold and save a tower. Then just head back to the lane your team is pushing.
I also love using it to scare people away. If my carry is dying, I drop the circle right where they are headed, people run away from the circle, and my carry gets away.
And finally, it's great for reviving and rejoining a team battle. It can create a virtual 6v5 if you die in a team fight, you can revive, drop back into the fight and most likely win, considering you just got a free life in a pivotal team fight.
It has multiple uses. Don't just try to drop on people to get the damage, because chances are you're not getting it. Any damage it deals is bonus. It's main purpose is to give him elite mobility, support of other teammates and ganking ability.