How to set up CB so a new user created from a membership manager is synchronized

We use a membership manager plugin that creates a new user after subscribing. Our question is how best to configure "Allow User Registration" so the CB User Profile is synchronized. I don't think we'd want to have anyone create an account using CB.  Should the field be set to "Yes, Independent of CMS..." or something else?
As a follow up question, ar the Joomla and CB user tables synched automatically or if not, what should we do to have that happen as soon as possible once the CB profile is created?
Thanks for any help and insights.

If possible I would recommend overriding the registration process in that extension to use CB API. The API to do this is documented below.

www.joomlapolis.com/documentation/127-community-builder/279-tutorials/18362-registering-a-user-through-cb-api

As a follow up question, ar the Joomla and CB user tables synched automatically

No, they are not synchronized automatically.

or if not, what should we do to have that happen as soon as possible once the CB profile is created?

You'd basically need to act on whatever event they have available for user registration, load the CB user object, the immediately store it. That would synchronize them. This can be as simple as doing the below CBs API has been loaded.

You'd probably be able to synchronize them using CB Auto Actions easily. Depending on the event though you'd need to be careful. CB user store runs normal Joomla user store events. So you don't want to accidently cause an infinite loop due to events.

Worth noting we've big changes coming regarding this with CB 3.x. We'll have more details when the time comes, but in short there won't be 2 profile storage logics anymore. CB having its own storage is a product of Joomla 1.x days when profiles couldn't really be extended. Now that they can be we'll be going in that direction.

Thanks a million Krileon, your recommendations are very comprehensive and we're excited to hear about the upcoming CB3.
Much appreciated!

Unfortunately, we are unable to override the user registration process in the plugin we're using.

Given that, what should the setting on the CB configuration field "Allow User Registration?"  We don't want to have anyone create an account using CB.  Should the field be set to "Yes, Independent of CMS..." or something else?
Thank you for your help.

Are you using Joomla's registration or another 3rd party plugins registration? Normally to disable registration you'd set that setting to be same as the CMS then disable Joomla's registration. We don't have an option to explicitly disable CBs registration while keeping Joomla's as from the context of CB that's a non-functional CB install. If that's the case you'll probably just need to use CB Auto Actions to redirect away from CBs registration to Joomla's.

To be honest your life might be exceedingly more simple to use CB Paid Subscriptions if you need subscriptions. Is there a feature we're missing?

Maybe another option is if you don't need to collect payment at registration time you could use CBs registration then after they register or on first login send them to subscribe?