I have successfully published a (very simple) Instant App linked to my personal website.
When I click on my website\'s link, I was expecting the app to start directl
We call this screen the "speed bump". It's a security feature. You're right in noticing that it doesn't always trigger. But there's nothing you, as a developer, can do to control whether it shows. The intention is for it to be a black box from your perspective.
This is designed in my opinion to happen at least once to give the user an opportunity to decide what to use: either browser or the instant apps feature.