systemd-update-done.service updates the file modification time (mtime) of the stamp files /etc/.updated and /var/.updated to the modification time of the /usr/ directory, unless the stamp files are already newer.
Services that shall run after offline upgrades of /usr/ should order themselves before systemd-update-done.service, and use the ConditionNeedsUpdate= (see systemd.unit(5)) condition to make sure to run when /etc/ or /var/ are older than /usr/ according to the modification times of the files described above. This requires that updates to /usr/ are always followed by an update of the modification time of /usr/, for example by invoking touch(1) on it.
Note that if the systemd.condition-needs-update= kernel command line option is used it overrides the ConditionNeedsUpdate= unit condition checks. In that case systemd-update-done.service will not reset the condition state until a follow-up reboot where the kernel switch is not specified anymore.