You earn the stamp by simply beginning the event in game (you will need to progress in the game far enough to unlock Ariel and build the town square building). The cap is awarded for completing the event's introductory quest with Skippi. Neither gives a notification in game, but you will get a neomail on site when you earn them. As a reminder, this is a limited time event so these rewards will only be available until June 30th.
BUT WAIT, THERE'S MORE! Previously limited time events have only been available in the Android version of the game, but this one is also available on iOS devices. Up until this point, iOS have had limited builds available through the TestFlight app, but the Island Builders app is now live on the main app store. If you were previously playing through TestFlight, you will need to download the app via the main app store, no update will display in TestFlight. This marks the end of the beta stage for the app! Only two years later. This also means that paid features of the app are now live on iOS.
Update: It appears that the iOS may be limited by country, and the United States is not part of the initial release group. We'll update you if that changes. To test if you have access, you can follow (you need an account to see links)