It sounds like you might have given your users too many role capabilities. They should have either Add Entry and Edit Entry or Add Entry Moderated and Edit Entry Moderated capabilities. See the doc page for for configuration of Link for more details.
I see you have Form too, make sure you follow the configuration instructions and take note about the special instruction for when Link is installed.
Lastly, both Link and Form were very recently updated. I highly suggest making sure you have the most current of each installed. You can download them from your purchase history. OR apply the updates in the WP admin if you activate your support license keys on the Connections : Settings admin page under the Licenses tab. Activation instruction for Form. Activation instructions for Link.. After you activate each, you will be able to update on the WordPress Plugins admin page.
Hope that helps, let me know.