You can see the cause of the problem in the attached picture. When you flush, water from the tank jets out along the underside of the rim at fairly high pressure from both sides. When the two streams collide, they change direction and ARC through the air to the backside of the toilet, where they lose their velocity with a great deal of violence. This splashes the toilet bowl contents into the air. In addition to being a mess to clean up, this poorly directed flow does very little to keep the bowl clean and that spray is distinctly unsanitary, particularly if your digestive system is a bit on the runny side (my fellow vegetarians are probably nodding knowingly).
Step 1: The desired flow
Step 2: Constructing the flow modification device
I used a pair of cheap scissors to cut the the fin shaped piece below.