As several other people have explained there is no early pulling. I have sat at fates and hunts for 5 minutes before pulling, killed the monster, and started leaving and still people are showing up asking for invites. There will always be someone running behind or that got the notification late.

If you see a shout go out about a fate and you take your time, then you are to blame if you are late.
If you see a shout go out about a fate and you drop everything to get there and you are still late, then get a better notification network.