After coming across this topic today, I did a quick bit of research on the subject of small pulse jets.
Assuming for the moment that the Himmelstürmer did indeed use two small pulse jets, rather than two small low powered liquid fueled rockets, as some sources seem to suggest, there seems to be two main ways, based on the technology available at the time, that they could have approached the problem (based on the traditional pulse jet that is, see further below):
Pulse jet with aspiration-
In this type of pulse jet, the fuel is drawn into the engine through an atomizer by the air which enters through the intake. The main advantage of this is that it is very simple and requires no fuel pump or other ancillary equipment. It also doesn't require that much operator interaction (just turn on and off). Therefore it's the most likely approach to have been used with regards as to the (pulse jet based) Himmelstürmer. The three most likely fuels, IMHO, that might have been used by the Germans in this case are, in descending order of likelyhood, methanol, kerosene or diesel.
Pulse jet with injection-
Here, the fuel is sprayed directly into the combustion chamber where it then mixes with air that has already passed through the valves. This allows one to throttle the engine simply by varying the amount of fuel injected. The major downside is that it normally requires the use of a pressurized fuel system such as a bladder or pump. Given the available information on the Himmelstürmer, this would seem to be the least likely approach used, unless they went with a pressurized gas as the fuel (removing the need for a pump), and even then it's doubtful.
Now, there is a third possible approach that the designers could have gone with, that being the valveless (also known as a acoustic-type) pulse jet. However, while they can be quite compact, and easy to build, use and maintain, I'm not sure that fuel efficient valveless pulse jets were developed before the post-WWII era. Although, given the known operational requirements for the Himmelstürmer system, that might not have been a insurmountable problem in the eyes of the design team. For the moment though, I would tend towards the first approach described as being the most likely used.
Whichever approach they did use, one way they might have improved the jump performance of the Himmelstürmer is through the use of an augmenter placed in the pulse jets exhaust. This would improve both the amount of thrust produced as well as overall fuel efficiency. The major disadvantage of augmenters is that, beyond a certain point at higher speeds, the drag they produce can offset their advantages. On the other hand, at slower speeds (and/or in short hops!) augmenters can be very effective indeed. I'm not sure how advanced augmenter related research was in WWII Germany though.
