Widget data won't import with WP database.

Try hitting save on the widget again. Nothing else.

I’ve found I have to do that whenever changing the domain on a site with this widget. I’m almost certain it’s to do with how Widget data is stored in the database, and not the fault of this plugin in particular.

You might run in to similar issues in Text widgets etc. if they contained the URL of your old site, and were caught up in a Search & Replace of the database (if you did one).