Did you check the generator with your scope while the 5783 was still loading as well? The 5783 has a 50 ohm input impedance so I wanted to make sure your generator can drive a 50 ohm load.
I cannot look at your actual project right now...
When you start your acquisition the FPGA will immediately stream data to its relatively small FIFO. If you are not able to retrieve this data (DMA to Host) fast enough, the small FIFO will overwrite itself and that could explain a waveform like the one you see. There are error flags you can use to check for any overflow (both on the FPGA - a Boolean on your FIFO node - and on the host side). Make sure to monitor these to catch eventual timing issues.
Also if you pause or stop your host VI, you may still have data stored in the different FIFOs. If you don't clean (empty) your FIFOs when you re-launch your host VI, you may retrieve old data first. Another possible explanation for your jumping waveform. In any cases, correct error handling should help you identifying possible issues.