Well, I'm in the US, but I have always understood this expression (at least when used in everyday speech) to be somewhat negative, that is, used to describe negative behavior, or the behavior of those who foolishly copy others, or both.
"The police arrested the Smith boy for underage drinking last week. Well, monkey see, monkey do; his mother drinks like a fish."
"I can't believe Jack spent that kind of money on a car. Well, monkey see, monkey do; Bill and Jim bought themselves Boxsters, so of course he had to have one too."
[not a teacher]