If the site owners really have access to create the accounts themselves, then i'd have the 'Review Membership Requests' setting in the FBA Site Configuration turned off - and the users will be created immediately. If you turn the setting on, the requests
will be added to the 'FBA Membership Request Management' page. By default this is also only available to site collection admins as well, but it's just a regular list, so you can adjust the permissions on it.
If you find that users's aren't being notified of the account creation, you may not have SMTP setup with SharePoint properly. Email needs to be working if you use the Membership Request web part.