Pulsing SYSREF causes the AD9625 to start some form of 'count' output, as well as make use of the ls 4 bits (only 3-bits ( to ) shown on sync.png and sync_detail.png; PN sequence?). This occurs for a limited period (see sync.png) after both edges of SYSREF (U_9/U_1_n_2). NOTE: AC coupling means the first rising-edge of SYSREF is off the screen-shot, therefore the problem is only seen 3 times rather than the expected 4.
We do have problems with the SYSREF signal, and it needs to be changed, but it's the operation of the AD9625 that I'm interested in: the data sheet doesn't mention any change in functionality due to SYSREF. And it could always be a hardware problem ...
Disabling the SYSREF inputs gives the ADC operation that I would expect (see sync_no_sysref.png).