Why does my cocoa syrup overflow?

This is likely due to capillary action drawing the syrup up the tube from the bottle - viscous syrup + a narrow tube = strong capillary action. Since it's one of those pesky laws of nature, there's not a lot you can do about it.

You might try transferring the syrup to a container with a wider pump tube (since capillary action is stronger in a narrow tube). Or you could transfer it to a container with a tap attached (like a keg) rather than a pump, but that prevents you from using measured doses. Finally, by the looks of it, the nozzle on the bottle might rotate, so you might also try turning that to point upwards and hope gravity keeps the syrup in place.

Failing that, the only other alternative would be to keep a drip tray underneath the pump to catch the syrup, then replace it in the bottle, but I imagine that has food safety implications, not to mention being a PITA.

We had the same problem and it turned our to be due to the temperature changes in the fridge. The expansion/contraction cycle of the syrup made it drip. Does your sauce require refrigeration? If not, try leaving it at room temperature (which doesn't change as much as most fridges). We used a "min/max" memory thermometer for a few days and found that the temp in the fridge varied from 30 to 52 degrees (F). While the internal temp of most food is OK at that range (it apparently didn't spend much time at those extremes), the change was making the sauce leak out of the pump. This stopped happening with our new refrigeration unit.

Try loosening the lid to let out any trapped air in the bottle. It may be pressurizing for some reason.

If it is being exposed to excessive ambient heat, or is on top of something rather warm, it may be too thin due to the raise in temperature. Grab a thermometer and measure the temperature to see if it's above the recommended storage temp.

Is it near steam or other heat? If so, move it.