I highly recommend using a plugin like BackupBuddy or Duplicator when moving site as they take care of all the little things that need done when moving a site from one server to another. WP stores quite a few things in the options table that is site specific. One of those being role capabilities.
If you are moving just Connections from one site to another. I would do what you did, export the tables and then import them (as SQL files). The one thing though, on the destination site I would install and activate Connections first and when you do the import, drop all the Connections table first.
Any way to answer you question…
This should be able to be fixed by going to the Connection : Roles admin page and checking the Reset All Role Capabilities option and then clicking the Update button. That should reinstall all the role capabilities and set them to their defaults.