Gen Y version of a linen mill (10)

I believe the answer is:

millennial

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'gen y' is the definition.
Although both the answer and definition are adjectives, I cannot see how one could define the other.

'version of a linen mill' is the wordplay.
'version of' indicates anagramming the letters (another version of the same letters).
'a'+'linen'+'mill'='alinenmill'
'alinenmill' anagrammed gives 'MILLENNIAL'.

Can you help me to learn more?

(Other definitions for millennial that I've seen before include "Relating to a thousand-year period" , "thirtysomething?" .)

I've seen this clue in the Sydney Morning Herald.

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