The problem at the moment is users are having their aMember session expire before the third-party script session expires. When this happens and they are in the third-party script, if they click the "logout" link (which takes them to amember/logout) then aMember doesn't run any logout method and so they are not logged out of the third-party script, meaning they just stay logged in until the cookies expire. How can I set the expiry time of the cookies so that they run out at the same time as aMember sessions in the loginUser() function of a plugin?
By default aMember set session lifetime to 7200 seconds. (two hours) So you should modify other scripts timeouts accordingly.