If you are getting that message when trying to restore and/or migrate a site (usually only happens when migrating or copying a site), it could be caused by quite a few things. So please see the following troubleshooting steps.
1) Please try a different browser. Sometimes browser add-ons/extensions/etc can cause conflicts. Or perhaps your browser doesn't accept cookies. Also, please be careful using incognito/private mode of some browsers. As that option doesn't always save cookies and/or site data.
2) For the site URL, if you're using http at the beginning of the URL, please make sure that you are not doing anything on the server to force https. So if you're getting that session expired message and you are using http for the URL, please trying using https. For example, if you're using http://example.com for the URL, please try it like so: https://example.com
3) If there are any server side implementations like Varnish, XCache, Google PageSpeed, CloudFlare, mod_security, Sucuri Firewall, etc., they may need to be temporarily disabled for the time being.
If the site is hosted with Cloudways, some of their hosting packages use Varnish. So the following links may be of assistance:
https://www.cloudways.com/en/varnish-cloud-hosting.php
https://support.cloudways.com/most-common-varnish-issues-and-queries/
https://support.cloudways.com/how-to-exclude-url-from-varnish/
BlueHost also has some hosting packages that come with Varnish:
https://my.bluehost.com/cgi/help/turn_varnish_off
4) Please make sure that the importbuddy.php file is not renamed something like importbuddy(1).php. In such cases where the file is renamed when downloaded because there is one in existence previously. The file cannot be renamed. Also, the same thing could happen to the actual backup file when downloaded. So please make sure that it is not renamed either.
5) Lastly, try a different importbuddy.php file. Since importbuddy.php files aren't connected to any specific site or backup file, you can use an importbuddy.php file from any site (as long as you know the password connected to that other site's importbuddy). Just go here to obtain one from another site or even the site that you're migrating/restoring as long as it's still available:
wp-admin (dashboard) -> BackupBuddy -> Backups -> ImportBuddy (link in the upper right) -> Download importbuddy.php
And you can choose a different password at that time, if you do not remember your password that you initially set.
It's usually best if you get one from a site that is using the most recent version of BackupBuddy.