So I read recently about how when the Mongols invaded what is now Europe, Subutai was able to coordinate army groups 100s of kilometres apart. How was this accomplished? I have a mental picture of the Mongols as very primitive - is this incorrect? Is there a certain amount of exaggeration to the Mongol capabilities or were they as fearsome as they sound?
There were three components to their coordination:
Intelligence. Scouts and/or spies provided information about the region. This included details of routes, including expected speeds of advance along those routes and availability of grazing and supplies, and details of defences, such as the presence of fortifications and their strength and the deployment of the enemy army.
Planning. Armed with this intelligence, the advance into enemy territory could be planned. Breaking the army into multiple columns, each advancing along different routes allows higher speeds, and provided better grazing for the horses and more supplies for the men. In addition, if enemy movements or tougher-than-expected fortifications stalled the advance of one column, the other columns could provide assistance, preferably by cutting the lines of communication of the defenders or attacking them in the flank or rear. The intelligence about the routes allowed matching the size of columns to the grazing available, and the difficulty of the march.
Communications. With multiple columns advancing along different routes, communication between the columns was very useful. Communications were what enabled one column to assist another if needed, and to keep other columns informed of the actual (as opposed to planned) speed of advance. Communication was by couriers, so time was required when the columns were a long distance apart. Note that the pre-planning facilitated communication - since the difference columns new each other's planned routers, it was possible to send couriers.
I have a mental picture of the Mongols as very primitive - is this incorrect?
It depends on what you mean by "primitive". None of the above needs sophisticated technology - spies and couriers are low-tech. Getting it to work does require foresight, planning, and discipline, but the Mongols were no strangers to these.
In general, the conquest-era Mongols excelled at the operational art of war - the area between strategy and tactics. Tactically, they could do well, due to discipline on their part and the lack thereof on their enemies, but many of their enemies were tactically skilled as well. Excellent operational skills allowed Mongol armies to surprise their enemies repeatedly, by taking unexpected routes, bypassing strongpoints, and combining multiple columns to outnumber an enemy in a battle. Strategic performance was somewhat mixed - poor strategic planning contributed to the length of time needed to conquer the Jin.
For as good an overview of conquest-era Mongol military operations, at the operational and strategic level, as is realistically possible given our sources, see:
Carl Fredrik Sverdrup, The Mongol Conquests: The Military Operations of Genghis Khan and Sübe'etei, Helion, 2017.