In fact, I observe that may be its a refresh probleme
Because when, in the current siteaccess I can show the session value now but, if I can submit my forms again, the session value of current siteacces not change but if I change de siteaccess the value is updated in this siteaccess :s:s
I guess the behaviour you describe comes from the fact that the module is called on the wrong siteaccess. Setting SessionNamePerSiteAccess to disabled should make the system behaves like you want.
