I didn't try the AAM (Arduino Automated Measurement), but I fed the signal into my scope (*) to have a look.
While the DDS is not incredibly accurate at the extreme duty cycle and frequency given, I saw no sign of the dire discrepancy you are reporting. Maybe I did not look long enough, but when set to 0.01 Hz with 0.01 duty cycle I get pulses separated by about 100 seconds.
Verified in normal and roll mode several times.
The width of the single pulse appears to be less than 1000 ms, but it's close enough. There is a slight variation from pulse to pulse, but it's hardly noticeable.
As a side note: at 1 kHz the automatic measurements of the Rigol scope (they are based on the pixels shown on screen, not actual memory) are spot on. But this might have more to do with the fact that I had only two pulses on screen and not three, so there were more pixels to make a better assessment.
(*) The overshoot you see in the pulses is due to the fact that I fed the signal into the high impedance input of the scope. The generator behaves better with a 50 ohm termination, of course, but I do not believe this could have affected time measurements in a significant way.
P.S.
I thought I had many more screenshots, but it appears that when my Rigol hit sequential number 43, it decided it was not worth saving them anymore. Also when I tried to open the last screenshot taken on my PC it made it throw a blue screen of death. Not the first time. Really sudden death, everything but the mobo and cpu stopped, and that includes all fans. And the blue screen message says "windows has stopped to prevent damage to your computer". WTF!