I don't think any car has a hydraulic engine. The term most commonly refers to devices such as jacks that use hydraulics to operate. Many cars that used lifters and push-rods used to have "hydraulic lifters," but a 99 Corolla would have an overhead cam and not even have lifters.
I'm not sure what you are referring to and I have many years experience with cars and their engines. On the other hand, I have been very wrong sometimes.
reference.howstuffworks.com