Active reload cooldown triggers if you press reload, when reloading. It does not trigger if you don't press reload a second time. This way you can postpone the trigger, avoid unnecessary triggering and have it ready for important fights.
If the passive of your item would trigger Active Reload cooldown, the upgrade would actually be worse.
I also think the info-text "Triggers Active Reload Passive" is confusing. I assume it means that an instant automatic reload is like triggering a successful Active Reload?