Toyota Hybrid system has 2 electric motors/generators. Each one can generate electricity on it's own. One generator is coupled with front wheels and will either generate electricity or help pushing the car, depending on power demand, as long as the wheels are in motion and above some minimal speed this can charge battery regardless of Internal Combustion Engine. Another one is attached to transaxle and therefore to ICE, this one is responsibble for splitting output from engine between the wheels and itself. Since each generator is independent, one can act as electric motor pushing the car, another one can act as generator and charge batteries.
Up to 42 miles per hour the gas engine can be off, above that speed the engine has to be spinning, because if it wasn't the electric motor coupled to it would need to spin above it's maximum 10,000 RPM. The fact the ICE is spinning doesn't mean it has to be burning gas. Sometimes electric motor can keep engine spinning without burning any gas at all. You can read more how the whole system works at Toyota site but I don't have the links handy. You can find list of all acronyms used here at the top of the page, under "glossary" menu.