Do players make rolls with the dice simultaneously or just make a mad dash of individual rolls?
The very first paragraph of the rules answers your question. [Emphasis in original]


  Escape is a real-time board game. Instead of playing the game in rounds, each player rolls his five dice as quickly and as often as he can without waiting for his teammates!


You can see this in this game play video.

[I just picked the first video returned by Google. I haven't reviewed it for quality. I set the start time to a spot where the player on the right rolls dice twice in the time the player on the left rolls the dice once.]