I have Membership Pro set up to automatically update the user's Joomla user groups. However, some of the people testing the site have said they cannot use the site as expected because they do not have permission with their new member / user. When I check back, they do have permission and I have found that the issue is caused by a delay in setting the Joomla user group, which can be anything from a few seconds to a few minutes.
How is the Joomla group update triggered and can it be sped up?
What payment method you are using? If you are using payment method such as PayPal for example, the system will need to wait for notification from PayPal about the payment before it could update Joomla user groups
So this is really depends on the notification from payment gateway. In most cases, it should be just one or two seconds, but in some special cases (rarely happens), it could take few minutes.
For this, sadly, it's not in our control and we could not speed up it