They don’t work with satellites. They work the same way as your normal calls do.
When you are out of network coverage, it does not mean that there are no network towers nearby. It just means that your particular network’s tower is unreachable. So this is why you can’t make normal calls. By law and design all towers should be able to handle emergency calls from any phones no matter what network SIM card they use.
And bands are always shared within networks under mobile infrastructure sharing. For example, Vodafone would have a contract or deal with Idea and other networks like Aircel to share their bands in areas where Vodafone lack towers. So even when a subscriber is outside the coverage area of his network, the cellphone will keep pinging all the nearest stations. It just won’t show it on the display. And when you make an emergency call, any nearby tower with the strongest signal will be used.
But if you are in the middle of nowhere like the Sahara desert where there are no communication towers, you are in bad luck. You can’t make emergency calls.