When update interval is longer that machine's uptime, pamac updater should wait for enough time before annoys user.
I open my computer for roughly 12 hours every day before shutting it down and booting it up the next day. I find pamac update notifications annoying but I don't want to use outdated software for too long so I set it to 3 days. I expect pamac daemon to only notify me every 3 days but instead it annoys me every time I boot my computer up.
Suggestion
Every time pamac daemon is started, it should remember the moment of when it is last started (store timestamp to somewhere in disk), and countdown from that moment.