Instant messages are delivered the minute they are sent out, just like emails are received the minute you hit 'Sent.' Push notifications work in the same way. 

Once you click 'Send' on the New Campaign page, push notifications are immediately dispatched. This makes it impossible for a campaign to be paused, stopped or deleted once it is sent. 

This is also why PushOwl asks for a confirmation when you’re sending a new campaign so you can take a minute to be sure before it is pushed out to your subscribers.