Firefox and Safari browsers have a restriction that permission prompt for opting into notifications (Browser Prompt) can only be shown after user has interacted with the page. So if you "Browser Prompt" enabled on your store, PushOwl will not straightaway show it after the set timeout. It will wait for a click on the page (user interaction) somewhere before triggering the Browser Prompt.
Note: This doesn't happen in case of Custom Prompt because Custom Prompt already receives a click (user interaction) on "Allow" button before triggering the Browser Prompt.