I tested it again today and found out that the major portion of the delay was due to my stupidity in having the FIFO buffer for the serial port way too high. I tested it again and found it to react within 23 ms, a huge improvement. So obviously the controller was working correctly, or at least close to the designed 16 ms.
I do, however, think this makes for a good argument to improve the roborun software to increase it's resolution, include encoder counts in the log file, and add a time scale to the plot. I also think it would help to add some sort of documentation online showing the 16 ms delay.