Happens to pretty much everyone, it's adrenaline which gets you to react faster, your body cools down and your hands begin to shake from the muscles decreasing response time to movement.
It's your body's fight or flight instinct.
The reason that adrenaline kicks in is the fact that you've got things to lose as civillian, and you actively know this during the entire fight, you get stressed which releases adrenaline.
When you respond as an officer to a shootout, you've got basically nothing to lose, and the moment you realise this you're completely calm in any situation, because what do you even lose besides your virtual characters life which you receive back within 5 minutes or less depending on medics?
It's normal, in other words.
When you've been in enough firefights, you'll start getting used to it, and your body slowly stops responding to the stress, infact you get less stressed because you know more of what to do during a fight the more you learn.