No, this isnt normal. Fortunately the filter is molded so it channels the water back to the tank instead of the floor.
As stated above, this usually happens when the filters are clogged. I dont see any discoloration on either pad, so I assume either the filter pads or the whole assembly is new.
I would check the housing that holds the impeller and make sure it is fully seated. This filter looks like the one I have on my shrimp tank. If it is, you can remove the intake tube, then pull the entire housing the tube was connected to straight up and out of the housing. (Be careful not to break the impeller) The impeller should come up with it.
Make sure there is no gunk or anything from the factory (sytrofoam bits, plastic residue, etc.) in the channel that feeds to the filters, then reseat the housing and make sure it goes all the way down. The shaft of the impeller has a rubber piece on the end that seats into a small holder at the bottom of the filter housing and another at the top where it contacts the housing. If the impeller is not aligned correctly it could cause the housing not to seat properly and the water would not be fully channeled where it should be.
That SHOULD take care of your issue. If not, something is blocking the water from going to the filter pads and you will need to find the culprit and remove it.
Why do I love fish? Because every time I stare into the little world I have created for them, every problem I have just floats away....