The other day I launched an sp3 and after the animation I found myself unexpectedly right in front of the defender. I got combo'd into oblivion. Using a different champion in the same fight, after the sp3 my attacker was not only far away but also on a totally different part of the screen. I started to wonder what factors are involved and thought i'd do some testing.
I took a bunch of champs into RoL to toss sp3s at Winter Soldier. In all cases I launched the sp3 while my attacker was in the far left corner with their back against the wall. After the sp3 animation, i didn't touch the screen until WS was up and moving. I took screenshots of the moment play resumes and the moment WS gets up, just right before he makes his next move.
I found a ton of variation across three areas.
Position on the screen: the attacker might be at the midpoint of the arena screen, the far corner, about halfway to the corner.
Distance from the defender: some were quite far; some were practically standing over WS.
Movement: some attackers stand still until after WS is up; some start moving immediately. For those who move, distance varies.
Some examples:
Herc: near the far corner, lots of distance, starts moving

Mr Fantastic: about 3/4 of the way across, lots of distance, stands still

Abs Man: midpoint of the arena, very close to the defender, not moving

Tigra: midpoint, somewhat far, but moving and covering a lot of ground

Sauron: midpoint, close, moves a bit closer

So far it looks like it's champ-specific, though I obviously can't say for sure. This is just idle curiosity on my part... if anyone has any insight or theories, please feel free to chime in