The fact that water is not compressible means that the water moving in one direction is capable of exerting an extremely large force on the water moving in the other direction when they run into each other, which would bring the water to a halt as the hole closes. The interesting question is: why doesn't this happen?
Why would you expect that to happen? The hole in the water is an area of low pressure that the water is going to rush in to fill. Now that water has a lot of kinetic energy and momentum. Why would it suddenly lose that momentum? And how does water's incompressible nature help that? Surely, if anything, this contributes to the difference in resistance between the water and the air and help explain the spike that you initially see.
