After Effects always converts vectors to pixels because AE only renders pixels. When you turn on Continuously Rasterize the rendering order is changed so that transformations in the layer (scale is the most important) are calculated before the vector information is turned into pixels. This maintains good edges. You should take some time reading up on the subject. The search Help field at the top right corner of AE is a good place to start.
When you are working with raster art (pixels) like video, still images or illustrations made with something like Painter or Photoshop you must design that artwork or capture the images with sufficient resolution (number of pixels not pixels per inch) so that the footage will never be scaled larger than about 120% at some point in your project. If your footage is never larger than about 75% scale you are also loosing quality and the footage is too big. If you go scale over 125% it is areal good idea to use some special techniques to improve the quality of the scaling. If the layers are made 3D then the distance between the camera and the layer should be equal to but not much greater than the zoom value of the camera because moving the camera is doing the same thing as scaling.
When you get your head wrapped around these concepts it's a lot easier to design artwork and capture images that will render faster and give you better results than you can get if your images are too small or too large for the project. This even goes for vector art created in Illustrator. The closer the artwork is to the size it needs to be in the frame when it is in it's hero position the easier it will be to work with the images in After Effects.
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