Off-Chain Event Trigger

Hey together,
I’m wondering how these Event Triggers actually function. If we look at the Crowd Funding example of the Plutus Playground and call the scheduleCollection function it waits until the collectionDeadline is met and then creates a transaction in order to collect the funds during the collectionRange.
If I understand it correctly the triggers run Off-Chain on the client-side or in my wallet. But does that mean my wallet needs to be opened in order to execute the trigger properly.
Otherwise I would miss the the collectionRange and I’m not be able to claim the funds afterwards?