I have not done this, but this is what I would do:
Start stringing both ends just as you would a regular necklace-- start the white pearls with white thread, attaching them to one end of the clasp, and the Tahitian pearls with whatever color thread you prefer, attaching to the other end of the clasp.
When you get to the last 3 white pearls, string the final 3 pearls on without knotting.
Do the same on the Tahitian side.
You'll have 2 threaded needles meeting in the middle, where the white pearls meet the Tahitians, one with white thread and one with dark.
Then make an overhand knot between the two colored threads, thereby joining the 2 half-strands.
Now reverse direction with each needle. Back-knot the white thread through the last 3 white pearls (that's 2 knots between 3 pearls). Pass the needle through one more white pearl without making a knot. Trim the white thread, thereby hiding the tail inside that last pearl.
Do the same on the Tahitian side. Reverse direction, back-knotting between the final 3 pearls, then pass the needle through one last pearl witthoug making a knot, and trim the tail.
One possible modification to this:
Looking at the necklace photo, I see there is no dark thread showing at all where the white pearls meet the Tahitians.
If you want to preserve that look, you could make the two half-strands join on the Tahitian side of the necklace, instead of dead center.
To do this, string the white thread through the last 2 white pearls and 1 Tahitian pearl before making an overhand knot to join the two half-strands, then reverse direction with the white thread on one side and the dark thread on the other side.
That means you'll have to stop knotting between the last 4 Tahitians instead of the last 3. You want to make no fewer than 2 back-knots, for security-- unless you plan to add a drop of Hypo cement. I tend to avoid adding any glue to pearl strands, but some people do use glue. This might be the time to use the drop of Hypo Cement so that you only have to back-knot once, through the last 2 pearls on either side. Back-knotting makes larger knots, and these knots will be front and center.