I'm going to guess there're two things going on if Siri pops up while you try to listen to your voice mail messages. One of them is that you listen to voice messages by holding the phone for your ear and second of all you haven't turned off the option that has Siri start interrupting with you when you raise your phone to your ear.
There's an option to the turn that feature off and have Siri only start interrupting with you when you press and hold the home button for a long period of time.
That's the way I use it so it so I've never really noticed this problem. I turned that option off in the beginning. So go to your settings find Siri settings and turn off the option that has Siri turn on when you raise your phone and this problem will just go away.