The u sound in “unit”

In paragraph 165 of the 2nd ed. of the Simplified manual, the authors use a u with a bar over it to represent the sound of the u in unit and tell us that it is represented by e-oo (small circle plus oo hook) in Simplified shorthand.  In paragraph 192, the authors tell us that the sound of a u with a bar over it is often represented by the oo hook alone in Simplified and give 6 examples.  In 5 of the examples, the u is (where I come from) pronounced like the oo in boot so it seems obvious that it would be represented by the oo hook in Simplified (and the fact that these should be in a paragraph about the u with a bar over it is surprising; I’m guessing that in some parts of the English-speaking world, the u in those words is pronounced like the u in unit).  But the one remaining example is the word amuse.  The u in that word is pronounced like the u in unit and I would have guessed that it would be represented by e-oo in Simplified shorthand.  When the u is pronounced like the u in unit, is there a rule that tells us when it should be represented by the e-oo combination and when it should be represented by the oo hook alone?  I’m guessing that when a u that sounds like the u in unit immediately follows an m or an n, the u is represented by the oo hook alone.  The outlines for mutate, commute, manufacture, and manuscript in the Simplified dictionary support that guess.