I think the Alligator Indicator has been misinterpreted by Kite programmers as the offset of the averages have to be shifted horizontally(i.e into the future), whereas it is getting shifted vertically( which doesn’t serve any purpose). Please find below a screenshot of the same chart and indicator on kite and tradingview.
I use the Alligator indicator on the good old ChartIQ charts. And this works quite nice for me. I use mainly the three wise man strategies. You can take a detailed look at the Alligator indicator and its trading strategies here. Do let me know if you have any queries on this. I will try to help you out.