Logout issues with Domain Mapping

My network uses SSL with wildcard SSL for primary domain and subdomains that are domain mapped are using Cloudflare (don’t know if that is relevant or not). Domain mapped sites are not able to logout of their sites. It first appears that they are getting logged out but it cycles back to being logged in again. This has been like this for a very long time. The only way to get logged out is to clear cache. I would prefer to keep the Cross Domain Auto Login because our users belong to their own site plus our support site and do not want them to have to login again when accessing that site. Isn’t it possible to logout of their primary site that they originally logged into without clearing cache?