Note that the commodity index used is the old CRB index now called the CCI (which MacroBusiness reports on each morning through the Daily links post).
The remainder of the linked post above completes the picture with the older version of the index (re-weighted) and monthly correlations, which have almost always been positive.
From a historical perspective, commodities were once used to diversify a portfolio as they normally were a positive offset during a stock bear market and vice versa. The thrust of this rationale is the changing cost of commodities affected corporate earnings through margin expansion and compression.
As for the ASX8 (the top four banks and top four miners), the two asset classes must be positively correlated to produce any uplift in Australian stock market valuations.