the session name is composed including the siteaccess. Have a first look in site.ini:
[Session]
# Decides how the name of the session value is handled.
# Possible values are:
# default - Let PHP decide the session name, this also rules
# out the possiblity for per-siteaccess sessions.
# custom - Use SessionNamePrefix for name. per-siteaccess sessions are possible.
SessionNameHandler=default
# Whether the session name should be unique per siteaccess.
# By enabling this you will be able to get one unique login per siteaccess.
# Note: Will only work if SessionNameHandler is set to custom
SessionNamePerSiteAccess=enabled
In override/site.ini the SessionNameHandler is set to custom.
