ShiroKuro I've read, and had piano teachers agree, that it's best to read from the bottom up, i.e., from the bass clef up to the treble clef.
I don't think most teachers agree on this and I don't believe there are hard and fast rules like that. It depends on the patterns in the music.
Honestly, I don't think that I'm reading in any regular direction from the bottom or from the top. What I'm doing is more like trying to quickly find patterns at a glance and using that information subconciously while reading details. For example, if I see that the left hand is playing a broken chord Alberti bass for the next measure I just put my left hand in that position and play the notes automatically while focusing on the treble clef, then I look ahead to see how the pattern changes in the next measure and prepare for that. If the pattern is different I might do something different, for instance I might notice that the hands are moving together or appart in thirds or that the notes are repeated in a regular pattern up a fifth or something like that. You have to become good at seeing the patterns at a glance and acting on them without much thought while saving brain time for decyphering the important details. It's much like not thinking about the spelling of each word while reading text.
Maybe the "look at the bass first" advice is a way to get students to notice the bass chord changes quickly and focus on reading the melody. That might work in some music but not always.