I'm not sure what's going on with Autotune, but I wouldn't worry about that. I just manually checked your page for the issues that our Error Check tool would diagnose and I didn't see any issues.
Now, back to the main issue. When you authenticate with a social network, the profile data is immediately pulled in. We don't do any background processing of the data. So, if the user is being redirected back to the site and is logged in, it means our authentication and profile import process is complete. If the user's profile isn't shown at that point, but does show up a little later after hitting refresh, it means that there may be some sort of background processing of data on your server (a cron job to reformat photos or something) or there's caching on the pages that's not picking up the changes right away.
With all that said, can you describe the problem any further? What profile system are you importing profile data into? When it takes 20-30s to show up, how to you check this.. are you just hitting refresh in the browser over and over or something else? We've never heard of this issue, so we'll have to get as many details as we can to figure out what could be happening.
Thanks,
Alex