I've got the same problem as some others have been reporting. After activating the plugin, adding my login details and then choosing to start importing data from Tumblr, nothing happens at all.
Of course, as explained in the other thread, I visited the site after activating the import process, to call the wp-cron function. Of course, I also restarted the process several times, and I've deactivated and reactivated the plugin to no avail.
I've got 'top' running on the server, which shows no new activity at all. Netstat gives nothing. The Apache logs doesn't report anything either. This tells me that the plugin isn't even executed properly. But how would I know if the problem is in the script, or in wp-cron?
Any help would be great. I simply can't manage to do the import manually, and the image-solution for Tumblr Importer seems wonderful. Thanks!
Edit: Of course, these things have a way of sorting themselves out by themselves just by posting publicly about it. :) What I did was to inactivate all other plugins, and then running the import process. Since this is part of the standard wordpress troubleshooting process, the joke's on me.