Back when DL flew BOM-AMS I can confirm they used the insect spray on departure.
I can also confirm it was very, very necessary. I was there the first week the new airport was open, and have vivid memories of sitting in the lounge swatting mosquitoes with my passport. One of the lounge attendants was making a valiant effort with an electric bug zapper, but she didn't quite grasp the tech behind it and was carefully scrubbing all the newly installed but still not on flatscreen TVs and creating a cacophony of spark noises. Oops.
On the other side of the equation, I also distinctly remember on at least one other occasion being on an AMS-US flight filled with mosquitoes - and when I looked it up, the aircraft was indeed continuing onward from BOM. So the spray is certainly not 100% effective...