Hi,
Is there a reason why you are using '#profile-tab0' instead of '#custom-name' ?
yes, Easy Profile extends Joomla management (not replace), so edit profile and registration pages are the same of Joomla with many improvements (with plugins and javascript).
Default Joomla Template (from com_users) separates the fieldgroup and various user plugins in many HTML fieldsets, but these HTML fieldsets not have any ID, CLASS or name, so we not have any parameter to identify these.
Still, keep in mind that the output in registration/edit profile page can to come from many different plugins, so, we can't predict the output. For example: if output come only from Easy Profile we can add some hidden text that adds a identifier of each tab.
So we need to add simple number of tab with some prefix and something like only "tab1,tab2" prefix can create some conflict.