How you react to knowing the date of your death influences the date of your death in the universe where you learn the date.

The mechanism behind it should be able to calculate the new date in advance though

It's already taking into account billions of variables (if the date is sufficiently far away), billions + 1 should be easy

Then the date would have to be re-calculated because knowing this new date could cause the date to change in a different way, requiring another recalculation, etc. I guess it really depends in practice, might only be a few loops before it gets stuck on one date, could see it being an infinite loop though

Now I'm imagining a tablet that continually updates with the date and time of your death. Could be an interesting short story.

Rick and Morty did something similar in the episode "Edge of Tomorty: Rick Die Rickpeat". Morty got ahold of a crystal that showed him what his final moments would look like, and the vision updated as his actions changed his future.