When I first started in Product Support, I struggled with how to respond to emergency issues. My instinct was to panic - these were urgent problems, clearly I needed to respond in a way that properly respected that urgency. But that instinct led me astray. I found dealing with the emergencies so stressful that I started delaying my initial response to them in order to avoid the stress, but of course all that did was make things worse (and get me a well-deserved admonishment from my lead).
The trick is to keep in mind that emotions are just signals. The emotional response of panic is just a signal of importance - once you recognize the importance, the panic serves no other useful purpose and just drains you. You do need to move things forward and get things done, but it doesn’t help to burn a bunch of emotional energy along the way. There’s no need to perform urgency.
This gets easier to do over time as you resolve more emergencies, train yourself that they can be solved, and gain confidence in your own abilities. But it’s important that new Support Engineers not be expected to handle their first emergencies alone. They should first shadow a mentor on an emergency, so that the mentor can model the correct response by focusing without obsessing and progressing without scrambling. Once the new engineer is ready to take the lead, they should still be reverse-shadowed by the mentor who can keep an eye on them and help them keep the ball rolling without reacting emotionally. Only once they have demonstrated the ability to keep calm and carry on should they be asked to fly solo.