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 Killing Amethyst should work. Bring up the list of recent activities and swipe right Amethyst. 
 Its nor a bug bur a feature 
 I have this problem too, even if I log out, it still shows as playing 
 App being in memory and phone having some active session cookies are orthogonal to each other. In Android, killing the app should kill dependent activities unless they are other apps actually. In this case, if the media player is playing the video, killing the app might not help.

Either way, please file a bug report ;) 
 App being in memory and phone having some active session cookies are orthogonal to each other. In Android, killing the app should kill dependent activities unless they are other apps actually. In this case, if the media player is playing the video, killing the app might not help.

Either way, please file a bug report ;) 
 Did you try force stopping the app? Usually works for me. Long press the amethyst icon, click the little "i"  then force stop at the bottom right