Was this plot point not clear to you watching the movie?
I guess not.

If everything is exactly the same, then the way she carries herself would be exactly the same.
McCOY: ...micro-miniature hydraulics, sensors, and molecule-sized multi-processor chips. ...And take a look at this!
CHAPEL: Osmotic micro-pump, ...right here. Even the smallest body functions are exactly duplicated. ...And every exocrine system is here, too, ...even eye moisture.
ILIA PROBE Deck ...er.
SPOCK: Fascinating. Not 'Decker-unit'? ...Gentlemen.
KIRK: Will.
SPOCK: Exactly. It's a programmed mechanism, Commander. ...Its body duplicates our navigator in precise detail. Suppose that beneath it's programming, the real Ilia's memory patterns are duplicated with equal precision.
KIRK: They had a pattern to follow.
SPOCK: Indeed. ...They may have followed it too precisely.
KIRK: Ilia's memory, her feelings of loyalty, obedience, friendship, ...might all be there.
Why would 'precise detail' not include how she carried herself?