Depending on whether you start from the Asana side or Reclaim side, you will see a white background with a button that says "Click here to finish the integration", but the integration is still not set up.
This can be determined when going back to Asana, you get a warning that says "Waiting for authorization" with a "Connecting..." button loading.
The likely causes for this are:
You are installing the integration via Asana's desktop app.
You have a pop-up blocker on your browser.
How to fix this
Ensure you are installing through your browser rather than Asana's desktop app.
Disable any pop-up blockers in your browser.