tl;dr Time zones.
While tracking error (per xirt) may be significant, a more fundamental issue in comparing these movements is simply timing. Looking at a daily up or down move, you have to consider: When was the last quote reported? When was the "previous close" from which the change is measured?
In principle, at every instant of time, there is a price at which a buyer and seller would agree to trade an index, whether or not there is an exchange open to do so. The price fluctuates 24/7 based on news and sentiment. These fluctuations are revealed when an exchange is open -- like pulling back a curtain to see something that was in some sense happening anyway. For many major indexes, electronic futures markets make this visible at least "24/5".
Even after the Chinese markets close (and the closing index level is reported) at 3 pm China time, global economic and financial developments continue to affect the price at which traders are willing to buy or sell a Chinese index -- see this related question. Thus, the price at which a corresponding US-traded ETF closes at 4 pm New York time (later on the same calendar day) may be quite different. In turn, when you look at quotes on the following calendar day, even at the same instant, the percent moves stated for the index and the ETF may be quite different because of the different baselines.
So more specifically, it should be possible to make a chart of the Chinese index and of the ETF (using say 15-minute bars) on a 24-hour-per-day UTC time axis, rescaling the prices to reflect the ratio that the ETF seeks to maintain to the index. At some times, only the index is quoted; at times, only the ETF is quoted; at times, both; at times, neither. The combined chart should show bars nearly overlapping when both are present. That is, up to tracking error, the available quotes from each source are partial windows onto a common underlying 24-hour price action. You can then visualize what each seemingly discrepant "percent change" means on that chart.