Check out what happens when I select dots.
1) Horizontally the dots are spaced 200ps / 5GHz apart. That's significantly faster than my 1GHz sample rate. That suggests the ADCs might support timing much finer than the sample rate, which might mean the hardware is capable of equivalent time sampling.
2) There are some very tight vertical groups.
Together these suggest that the trigger-out jitter is grouped to some multiple of the ADCs' clock - probably the FPGA's clock. Perhaps the trigger-out logic runs on a divided clock. That's really weird though, since the trigger in seems quite accurate.
Disclaimer: I don't know WTF I'm talking about.

Marmad, might you could give us a screen shot of the trigger pulses on dots mode at 2ns/div?
Edit: Note that this also had 500ms of persistence.