Incorrect.
The ultimate does not actually "happen" until Illaoi finishes the leaping animation and then slams into the ground.
The ultimate also does not do anything except make the tentacles.
The only way to make the tentacles swing is through either hitting something with her W or by having a Spirit out, which will cause all tentacles in range to hit it. There should not be a Spirit out in the first place, because both parties should have been able to dodge it.
The W range is quite short, and the tentacle(s) will not swing until she actually hits the target, which is to say, the leaping animation is just excess time for the Illaoi player.
Also, she won't escape if you flanked her in the first place between your tower while she was pushed up (which she'd naturally do through nature of her Q waveclear/Ws/occasional slams from Vessel-targeting). Like I said, once she's relatively close to her enemy's tower, flank her and push in as far as you can to increase the distance you'd have. Once she inevitably throws out her E, whichever party she aimed it at then dodges.
After said point, she will be forced to burn her ultimate sooner or later unless she wants to have no chance at all, at which point she'll burn said ultimate. Now, since said tentacle pit from her ultimate will be fairly close to her enemy's tower , just back out through the lane towards her tower. The tentacle pit is now out of range, but she is still trapped between the two of you. Also, if reactions are fast enough, one or both of you could potentially back out of the range of her ultimate's slam in the first place before it even spawns tentacles.
CC her and start hitting her. One of you should have some method of applying GW, because both the laner and jungler really should not be AP (AKA, one of them should have Executioner's Calling). Start damaging her. She has no mobility nor escape nor any other realistic mass damage at this point. She will either die or burn Flash if it's up or take a hefty bit of damage.
Sooo...