To link the tree and the character you can use UIDs.
Give the character a variable called TreeUID
Then, when the character collides with the tree set TreeUID to res_Tree.UID
When the character's timer goes off use Pick Tree By UID: character.TreeUID to pick the correct tree
However, I can anticipate there being a possible problem if the character's collision box changes during it's animation. It may repeatedly collide with the res_tree as it's frame changes. Try opening the game in debug mode so you can get a better look at what the timer is doing
I was about to do that, but I decided to re-check the Debug Preview one last time. It turns out the "gatherResource" timer is being reset every tick, which I didn't notice before (I only just discovered the Watch tool!):
It tries to go up, but only ever gets to 0.1/0.2 seconds before being reset. There aren't any other interactions with that timer in the Events Sheet, except for the "On Timer" condition below it.
The parent event to that set-timer-event is just checking if the Human has a variable of job->woodcutter, in case you were wondering. No reason for any clashes.
Thanks for your help so far!