Unlike a roof-top aerial for terrestrial TV, which doesn't use any power, a satellite dish requires power to the 'LNB' (which is the 'sticking out bit'), which goes up the same coaxial cable that your TV signals come down. That's because the LNB has to switch between different channels as you change channels on your TV or set-top box, in order to match the correct frequency and polarisation of the channel that you want to watch. So you can't simply split a single satellite cable, as the LNB can only be matched to a single channel at any time.
However some (many?) dishes have 'dual' (or even 'quad') LNBs, with a separate cable for each channel being viewed. (Even if a dish only has a 'mono' LNB, it can normally be replaced with a dual or quad type but it will still need separate cables for each bit of the LNB to work with).
So, although (when equipped with a suitable LNB) you can use your satellite to receive different channels simultaneously, you'll almost certainly need some extra cabling to go with it.
I'm not sure how the product in your Amazon link is meant to work but I certainly wouldn't trust it and, anyway, I note (from the illustration) that it requires an amplifier in between the dish and the splitter; it can't be used on its own, it seems.