Eb Tuning - Justin's Blues Lead book

I just purchased Justin’s Blues Lead book. Looks cool and I am excited to give it a try. I guess this is a baisic question but I wanted to make sure I understand. First song "All Along the Watchtower’ the notes say to tune down a half step(Eb). All strings get tuned down(Eb, Ab, Db, Gb, Bb, Eb).

The chords in the book for intro solo show A B C#m. If I use Root 6 bar chords it sounds like I play the chords at 5th, 7th, 9th fret (which is normally A B C# but are now tuned to Ab Bb Cm which sounds correct to the recording. I was playing this at the 4th, 6th, 8th fret prior to changing the tuning.

So is it correct to say that the book is showing where to play as if you were in standard tuning and not the actual pitch to play? Is this the standard notation that I would find in other TAB book? I never tried alternate tunning prior to this so this is new to me.

Thanks,
Phil

Yes.

Same as if you’re changing the key of a song by using a capo, you then play the same notes and chord shapes, but with reference to the capo, instead of the nut