By default, when an event is triggered, the Intercom Sync plugin places the event in a queue to be sent asynchronously. This is best practise to avoid a user being delayed as the event is sent to Intercom. In general, assuming you have a medium to high traffic site, and WP Cron is being called correctly, your events should send in less than 5 minutes.
If you wish for events to send immediately, and this is not recommended, you can enable synchronous events in the Intercom Sync plugin setting page. To enable them, ensure the relevant box is checked and you click Save Changes.
Intercom Sync uses the Action Scheduler Library to queue all actions of the plugin.