Do you use “Admin menu access” add-on from User Role Editor Pro and blocked some menu items for this role?
A lot of User Role Editor Pro users work with AVADA theme and do not report any problem.
In general if you just added a capability to a role, the rest work makes WordPress itself and theme and/or plugins which check user role and capabilities. So if a problem is raised really for this reason you can ask support question to fusion-builder plugin developers too.
I can investigate the issue in my test environment if you provide me access to the database and site files copy – via DropBox or GoogleDrive (support [at-sign] role-editor.com)