PopupAlly Pro attempts to store the styling information in a file for faster performance when your site is loaded in the browser. However, it will return this error if WordPress does not have write permission on the server. (Another example of this is when you install plugins, you are prompted to enter FTP login information).
To get past this error message, you will want to enter the FTP information into wp-config.php.
Here is the WordPress documentation on the topic: https://codex.wordpress.org/Editing_wp-config.php#WordPress_Upgrade_Constants
The variables you need to define are: