I never telegraph my stress to my team members but used to often do it around my peers (managers on other teams).
Probably because I thought they could empathize so they'd be a sympathetic ear. A few complaints to the CEO about me later and now I've learned to do what the author describe. Even if the person is not someone who reports to you; just go get a coffee, take a walk, etc.
I am lucky in one regard though, Our CEO flat out told me if I need to stress out around someone do it around him. Which seems healthy and more productive then bottling it up.
(Get fat instead?)
Now I handle this with - Cashews in my desk - Frequent water and coffee breaks - Minimum 15 minute walk outside during lunch
It's worked out pretty well for me so far.
For me, I tend to talk faster, raise my voice a bit, frown more, and generally behave more combatively.
So basic things like slowing down, relaxing my expressions and smiling more (even and especially when you're on the phone!!!) go a long way to not only changing how I present myself, but also changing how I feel.