Those indices are there to give you a comprehensive view of current performance of the asset pairings at a glance. From the shots you can see that all the the crypto assets are paired with the USDT(stable coin).
With Satoshi Index, there's 50% allocation of weight pairing on BTC/USDT alone. The second heaviest is ETH/USDT with 20% weight, then followed by a series of 5% weights on others. Now what this weight pairing does is to give you analytical view of all those selected pairings in terms of their current market performance. Green colour indicator means Bullish(price rise), Red colour means Bearish(price fall). BTC/USDT takes the greater portion of 50% so in most cases when BTC is bullish you'll observe the colour is Green, and when BTC price is falling it turns red.
The Major Index is what most investors and traders use. This is because the pairings are equally distributed among the top 6 trading assets; BTC, ETH, XRP, LTC, DOGE, and DOT. Again, all paired against the USDT. So at a glance at the Major Index you'll have an idea how those top 6 assets combined are performing.
Finally, Composite Index combines more pairings as you can see, 23 pairs. These pairings are also equally distributed and all paired with the USDT.
So in a nutshell, it's possible for one index to look Bullish and the others look Bearish at any given time because of differences in weight distribution and number of pairings. Also note those dates on top of the pairings are when the pairings were last modified. In future for instance, when CORE is listed on MainNet and performing well, it will be paired with the USDT and be included in any or all of the indices we see now. Maybe the Satoshi Index may give greater weight of 50% to CORE. In that case we'll see something like CORE/USDT(weight of 50%)