I believe you're going to keep running into issues as even with the parameter updating, your viz will continue to use established session with 15 minutes beings your lowest possible cache setting. The first things I would try are to remove any references to a session ID from your embed URL (i.e. "#1") and add the URL parameter ?:refresh=y
This blog post has some interesting info on refreshing in Tableau Server:
P.S. Be sure to make all helpful and correct responses as such using the buttons provided.