Pointing your own domain at an app you built with AI
You buy the domain from a registrar, then add two or three records telling the internet which machine should answer for it. The change is not instant because the previous answer stays cached around the world for a while. An hour of looking broken is normal.
The one rule
Register the domain in your own name, with your own card. A domain somebody else bought on your behalf is theirs, and recovering it ranges from slow to impossible. Everything else in a project can be rebuilt. An address people have already learned cannot.
Why it looks broken for a while
The internet remembers the old answer for as long as it was told to, and different parts of the world let go at different moments. It can work for you and not yet for a friend abroad. Nothing is wrong. Make the change once, correctly, then leave it alone for a few hours.
The most reliable way to turn a slow change into a genuinely broken one is to keep editing the records because it has not taken effect yet.
What good looks like
A tool should show you the exact records to add, then tick them off as it sees each one arrive, so you can tell the difference between a mistake and ordinary waiting. Ura shows the records and the ticks; it does not reach into your registrar and change things on your behalf, because your domain account should stay yours.