In a bubble chamber, or something similar, which is what produces those photos of the particle tracks, a magnetic field is applied. Charged particles curve in magnetic fields as the magnetic field provides a centripetal force on the particles. This force acts in opposite directions for oppositely charged particles, hence the two particles produced curve in opposite directions.
During pair production, momentum must be conserved as there are no external forces acting on it. Both linear and angular momentum must be conserved so they "curve" away from each other in order to conserve momentum.
Of course angular momentum is conserved, but that's not why they follow curved paths.
They curve away because they are charges moving in a magnetic field.