The rule seems to be very limited if we look at the semantics of the sentence. I use -'egh and -moH on yIbItHa'qu because it's a command to make yourself un-alarmed, something to actively do. The command with yIbItqu' is a command not to enter an alarmed state, something that one doesn't actively do to oneself. I'm not entirely sure that -'eghmoH is needed here.
Maybe it would be better to say yIbItqu'choHQo' Don't change state to being alarmed.
In general, I just don't know the answer to your question of whether the negative form requires -'eghmoH. If often feels wrong.

Thank you for clarifying!

I know there is no simple answer, I just want to be sure I've understood your explanation. You tend to use *-eghmoH* when the subject can control or influence the required change. *Cause yourself to be un-alarmed or relaxed* makes sense, because *becoming relaxed* is something one can actively do (with exercises, analysis etc.). *Don't cause yourself to be alarmed or nervous* makes no sense, because *becoming nervous* is something one cannot *cause*, something one doesn't control, it's a state one is brought to and therefore you cannot command someone not to cause a state she or he is not able to cause anyway. Or am I missing something here?

Yes, that's pretty much what I mean.

-- 
SuStel
http://trimboli.name