Whenever you feel like it. Its worth considering a few things when saying this.
The underlying package manager does not force you to reboot - though /var/run/reboot-required
will tell you if its needed.
Linux will hold on to the old version of the file till nothing is using it , so typically a restart is for kernel upgrades, and maybe drivers/modules.
Finally there's a philosophical difference between linux (designed for powerusers, and folks who boast about uptime and reliability) and a desktop oriented OS - windows server probably wouldn't force a reboot either.
As such, in linux these reboot warnings are considered recommended not essential and its informational. There's nothing stopping someone from writing something that ran sudo reboot for you though.
Found this which says Software Updater should launch automatically ... when ... security updates require a restart to finish installing, and it has been at least 24 hours since you were told about this; or ... non-security updates require a restart to finish installing, and the “When there are other updates” interval has passed since Software Updater was last open (either automatically or manually) but systems don't seem to go respect it or I'm understanding it totally wrong. Accepting this as it provides more insight
– pun – 2016-06-02T05:59:02.200