Ambimodal transition states in some organic reaction pathways
Why do these ambimodal transition states occur?

I don't know that there is a general reason for that. Potential energy surfaces are complicated. Very often, there is an abundance of local minima, separated by potential energy barriers. It is similar to what happens with mountain chains and valleys, but with many dimensions.
One could argue that the opposite could be asked: why would there be a single minimum associated with each and every barrier? Why would there be exactly a single downhill valley behind each mountain chain, instead of, sometimes, two different valleys being similarly accessible, once you climb over the top of a hill?

How does the situation differ from normal transition state theory?

Transition state theory is a useful simplification, assuming a simple potential energy surface. It is useful because, at room temperature, the energy differences in the different possible paths are very often sufficient for a single reaction pathway to predominate, so that others effectively do not happen. When the temperature is comparable to the difference between the energies involved in different possible reaction pathways, the situation is more complicated.