She thinks by imitating the click, she gets a treat. Its her way of saying Give me a treat!
In the behavioral aspect, I'd recommend to ignore it. Completely ignore it or future trainings could be difficult.
Have you tried target training?
I've actually found that praise plus treat gets better response than clicker plus praise plus treat.
I am getting a bit more success with flying to command with target training. One of the main problems I have with her is attention span. Not sure if it is a lorikeet thing (they're notoriously ADHD!!!!) and the only thing that I can use as a treat which they go nuts for is the loritreat bottlebrush nectar which is of course as sugary as you can get!
She is really keen to please and loves it when I praise her and it didn't help that I burst out laughing when I realised she was actually copying the clicker rather than realising it was the confirmation that she has done what she is supposed to do and will be rewarded for it. So I'll put my hand up on that one as I more than likely at that point reinforced her behaviour accidentally.
She has made a game of doing the noise now so the clicker has been abandoned and I am using a certain tone and phrase to pre-empt the treat. The training is really short, I only do a couple of minutes max due to the issues I have with her attention span and once she's has a few licks of the treat she goes hyper.
Possibly both. 
