No, that's actually the more common way to fit the nut.
The two most common ways to fit the nut to the fingerboard are "shelf" style and "slot" style. Shelf style is what you've shown above. The fingerboard is cut off right at the "0" line, and the nut seats on the neck wood, right up against the end of the fingerboard. This style is used on most instruments that aren't Fenders.
Slot style is Fender-style. They rout a 1/8" wide slot in the fingerboard, about 0.100" deep. The side of the slot towards the frets is exactly on the "0" line. The nut blank is 1/8" wide (thick) and it is glued right down into the slot. The fingerboard usually extends about 3/8" beyond the back side of the nut. The bottom of the slot is usually cut flat, straight across. But on some model Fenders, it's curved, following the radius of the fingerboard. In that case, the bottom of the nut also needs to be trimmed to that curve. Slot style nut installations are used on almost all Fenders, and many Fender-copy instruments.
On a slotted fingerboard you get from LMI, they cut you a "0" slot so that you know exactly where it is in relation to the other slots. If you want to do a slot style nut, you specify the fingerboard with about 1/2" of extra wood beyond the "0" slot. Then, when you get it, you cut (or file) the 1/8" wide slot for the nut right on the outboard side of the "0" slot. It's very important that you don't harm the inboard (toward the frets) wall of the "0" slot. That's the precision surface that you need to maintain for proper intonation.
If you want to do a shelf style nut, you trim off the extra wood beyond the "0" slot. You have to do that carefully. You must maintain that inboard side wall of the "0" slot. Don't just bandsaw right down the "0" slot. You can use a fretsaw carefully, right in the slot. Or, bandsaw outboard of the slot, and then carefully block sand back until you are just touching the inboard side wall.