Jimmy nailed it. It's the subtle combination of relief, height over the last fret, nut height (and that's a great way to set it, JJ), and how you play the instrument. Guys with a light touch fingerstyle can get away with lower/straighter than some guy framming it with a heavy pick in his AC/DC cover band.
As you can imagine, the bigger B and E strings are gonna vibrate in bigger arcs than the D and G. So when we set the bridge for the string heights over the last fret, think of the plane of the 5 strings as tilted up on the bass side to account for this. That is, the bridge will be a bit higher on the bass side than the treble side. If you look at the nut slots, you'll see James accounted for this on that end, as the B looks as if it's a little shallow and the G looks a little deep.
My starting measurements would be around 1/8" clearance on the low side, and a bit less than that on the G side. Your results will vary, but that'll get you in the neighborhood, and you set that once your neck relief is where you want it. As always, on an Alembic, this is far easier than any other bass, with the adjustable nut and the one-piece bridge.