How are linked files accessed by AE as you work with them?

The source files are read when they are accessed, and every pixel on every layer is read from the source, modified by scale, position, rotation, opacity, and effects, then calculated to create a new image, eventually used to create the final render. It's the same way that all compositing apps work. Take the source data from storage, process it, and render a result. 

A few operations, like Rotobrush and Warp Stabilize, create a lot of data internally and bloat project (AEP) files. If the process (Rotobrush, Warp Stabilize, and a few others) takes a long time, it is almost always to pre-compose the layer you have processed, open the pre-comp, choose Composition/Pre-render, and then delete the Rotobrush or Warp Stabilzed comp. AE will perform better, be more stable, and the project file size will be a lot smaller.