The Hyundai system uses the electric motor mainly to assist the gas engine, first at startup, acting as a substitute for a torque converter between the gas engine and the transmission. Even when the gas engine is running, the car is moved initially by the electric motor until it the car is going fast enough for a smooth transfer to the gas engine. In times of low torque demand, like slow acceleration or at certain highway conditions like long flats or slight downgrades, the car can run in electric mode until more torque is required or the battery level gets too low. At all times the gas engine rpm is dictated by the speed of the car and the selected transmission gear. Toyota and Honda use much more complicated systems with more powerful electric motors. Their systems try to force the cars to use electric motors, using the gas engine mainly to power the electric generator. With Honda, the gas motor pretty much only drives the wheels at highway speeds above 65 0r 70mph. It has a fixed ratio transmission, so the faster the electic motor goes, the faster the car goes. The electric motor is screaming at above 10,000 rpm at those speeds and when the gas engine kicks in to directly power the car it is also screaming at speeds approaching 4000 rpm or more. That is why highway mileage is actually lower than around town. The other indicator that these cars rely mainly on the electric motors is that there is no reverse gear. They simply run the electric motor in the opposite direction, something that Hyundai's traction motor never does.
Toyota's system is even more complex. it has a cvt, but it is gear driven with a complicated planetary gear system that can go into overdrive, while at most times the gas motor is trying to maintain a sweet spot of between 2000 and 2500 rpm. Honda and Toyota can achieve slightly better fuel economy, but for me the power has the feel of driving a boat with an outboard motor.