Why do pidgeys and rattatas still appear even if not in sightings?

There are more possibilties:

  1. Your data in the tracker is not synchronized yet, but the information for the pidgey is already downloaded.
  2. It just spawned there.
  3. The list is already full with other Pokémon (can happen, probably not with pidgey or rattata but though).

When you reopen the App with a good Internet connection the tracker should be loaded accurately.