I can't find where I read about this information, but it was said that the new hunting tasks would work the same way as the old one in regards to the kill count. This means that if you're not in a shared exp range, you'll get the kill count only if you deal the most damage to the creature.
I did some testing to verify this information, since I couldn't find the source where I read it and these are the results on a dworc fleshhunter (max HP 85) weekly task, done by a party of a level ~700 (Player 1) and a level ~90 (Player 2) (aka they aren't in shared range):
- TEST 1: Player #1 did 1 damage with Thais museum rod and Player #2 killed the fleshhunter (84 damage).
Outcome = no kill count for Player #1's weekly task
- TEST 2: Player #1 did 36 damage and Player #2 did 49 damage.
Outcome = no kill count for Player #1's weekly task
- TEST 3: Player #1 did 49 damage and Player #2 did 36 damage.
Outcome = successful kill count for Player #1's weekly task
As shown in the picture, even if being in a party, if the players aren't in shared exp range, it doesn't always grant kills for the weekly hunting task even if both players tagged the creature (for bestiary it counts, but not for weekly tasks). So whoever dealt more damage to the creature, gets the kill count for the task.
PS. Just as an additional information, if the players are in a party with shared experience, then it works exactly like in bestiary. As long as all players in the party dealt at least 1 damage each to the creature, all members will get the kill count on the weekly hunting task.
Edit: not sure how to upload good quality picture in an answer, so here's a link for zooming in the image - https://imgur.com/a/ORTydPs
