It's interesting. To me it seems that both the authors are correct. In the example about talking children the tense doesn't matter much because it's evident anyway that the coming of the teacher was the reason for the children to stop thier chatter, which they apparently did just at the moment he came in.
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New2grammarIt's weird that the first pair is not acceptable whereas the second pair is fine.
my other book = ?the other book of mine
my other books = other books of mineThe first is definite; the second indefinite. Ant has the basic idea. See his post.
Let me repeat what I wrote. Note that your second equality is not something I claime