There are many studies of neutron distribution. Overall they show that with low current DPF, most neutrons come from collisions of the ion beam with the plasmoid. But in higher current machines, they come from collisions of ions trapped in the plasmoid with each other, which increase faster with increasing current. In FF-1 neutrons are very evenly distributed, showing that the ions are trapped.
The current starts next to the insulator because that minimizes induction and thus the amount of energy in the magnetic field. Currents always minimize the amount of energy they have to expend. Mother Nature is not lazy, just efficient!