It sounds complicated but it really isn't if you have been properly trained, if you understand it, and if you follow procedure. The guy in question was missing out on the last one and probably had been pencil-whipped on the first two through one of his superior system Euro/Brit buddies in the "Type Rating"!! training.
It's German engineering, designed to isolate component parts of the fuel supply system so that a leak or bullet hole in any one or even two parts of the tank system will allow at least one engine to keep running, supplied with fuel, until an emergency landing can be made. The aircraft was designed as a candidate for replacement of the military version of the BO-105. When the military forces didn't buy it for whatever reason, it was pitched to the civil market and has become a best seller.
It's really very simple: You turn prime pumps on, start the engines, turn prime pumps off and transfer pumps on. transfer pumps each send fuel to the supply tanks, which should indicate a constant quantity...as shown on the gauge. As you burn fuel the main tank quantity drops. If you land before main gets below about 150, nothing happens. But if you keep flying the aft pump gets uncovered, because you have a nose down attitude--unless you are hovering OGE, then the nose is up and the forward pump gets uncovered. When a pump gets uncovered (fuel level dropping) and runs 3 minutes dry, a signal is sent lighting up that pump on the caution panel--then you reach up and turn it off. As I said in my previous post, the guy went through some kind of hover/fly cycle that evidently had him elect to turn off both transfers and not turn them back on, EVEN THOUGH there was some fuel in the main. As a result, the engines started sucking down the supply tanks--they contain about enough to fly for 25 minutes or so. When the supplies get to a certain level where you have about 10 minutes of powered flight left, all kinds of cautions and warnings tell you so. The guy ignored them. Death ensued. I wasn't in the cockpit and you weren't either so it's stupid to try to guess exactly what happened. But one thing is certain, the guy ran it out of gas and stopped the blades in mid-air and fell to earth exactly like a brick. At the very least he ignored the most basic principle of powered flying, i.e.: TIME IN THE TANKS...when you take off with a certain fuel load, you know--or should know--almost to the minute (experience makes this easier) HOW LONG YOU CAN FLY.
Run your aircraft accordingly.
But again, in conclusion, although there is a lot more information on the EC135 fuel system, including fine points, technical data, it really isn't that complicated. It's one damned fine piece of German engineering and design and of the 15 or so types I've flown, I consider it the best of the lot.