Funky jazz saxophonist's tiny colourful family (12)

I believe the answer is:

hummingbirds

I'm a little stuck... Click here to teach me more about this clue!

'funky jazz saxophonist's tiny colourful' is the definition.
I can't tell whether this defines the answer.

'family' is the wordplay.
I cannot really see how this works, but
'family' could be 'bird' (bird family is a kind of family) and 'bird' is present in the answer.
The remaining letters 'hummings' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

I've seen this clue in The Independent.

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