This is a very difficult question to answer. Both words have "decrease" as synonyms.
I think that we tend to use "were diminished" as more of an EFFECT of some action than the active use of diminish as an ACTION.
You will probably want some more answers, but there may not be a logical reason that "reduce" sounds right and "diminish" sounds wrong. It's just how we tend to use them.
What an utterly unsatisfactory answer. I hope someone else can do better.
Interested in Language