This is correct!!!

Moreover! This is why breathing in the correct manner helps with physiological relaxation. (Look up diaphragmatic breathing). Especially with a slightly longer exhale than an inhale (example: inhale for 4 counts, hold, exhale for 6 -7 counts, hold) helps tamp down the fight or flight system (sympathetic nervous system) by activating the rest and digest system (parasympathetic nervous system).

The reason it works is that it is a backdoor way to communicate to your brain: hey, this isn't a threat. I'm fine. I'm not in danger.

Same principle, generally, as what is being discussed with using the paper bag for hyperventilation.