On the rare occasions when I need to scroll through previous searches terms, I can easily click on the search bar and then use the up/down arrows. But I rarely need to do that. Instead, what I do much more often is search, then navigate around that area.
So after searching, users should be able to navigate immediately by using the up and down arrow keys, the page up and down keys, CRTL Home, and CTRL End. The focus should not remain in the search bar.
There should be a way to modify the current default behavior. After all, customizability is one of the key strengths of Sublime Text.