Hi Dennis,
The export files does not actually contain any domain information, it is always relative to the root path (‘/’). Moreover they does not affect the search in any way. The result URLs are always requested via the get_permalink() call from the WordPress core. The index does not contain any URLs either, only the keywords. One exception is if you use the cache, make sure that is disabled/cleared and not copied from one site to the other. The instance export process does not copy that, only the options.
The license stands indeed for one end product, but the plugin itself does not limit the functionality in any way. You can still install it on any number of sites without problems. You can use it on any number of local/remote test installations as well. Only the automatic update feature is bound to one domain (which can be changed), but the functionality is not. It is only a legal issue, we cannot limit the functionality in any way 🙂
If the plugin cache is disabled, then the only possible explaination is, that somewhere on your local wordpress configuration the site URL is not set correctly. If you exproted one test site to the other, usually the wp_options database table carries the home URL from the first site. You can try forcing the correct URLs on the wp-config.php files, as well as searching the wp_options database for eny remains.