Okay, I see what's going on now. Because I had it enabled from the beginning, the whole fade process was started the INSTANT it was created, despite that I had the Wait Time immediately updated in the exact next action in the same event. So the wait time, as defined in the editor parameters, was counting down as I had it at default.
And, like you said, the Wait Time was getting updated, but it wasn't taking that info into account.
So I told it not to have the Fadeout behavior active at first - only after I updated the Wait Time did I enable to Fadeout behavior. Now it's working as I wanted it.
Thanks for helping me to work it out!