Yes, the button in the photo has what button-collectors call a "birdcage" shank. The "turret" shank gets its name from looking like a (modernday) warship artillery turret. Minus the cannons, of course.
You requested a date-range for your button's version of birdcage shank. The photo below shows a World War 2 era French Navy button's birdcage shank. Yours appears to be a present-day version, in which manufacture was simplified by using a one-piece cross whose arms are folded back to form the "cage," instead of two crossed wires brazed together.
For anybody here who doesn't already know:
The "birdcage" shank is most often seen on French-made buttons.
I like "birdcage" better on this one. These were made in the 1830-40's for the most part. The earlier "turrett" style was used about the time of the revolutionary war and is the shape of a hockey puck but much smaller with two drilled holes going through it to make a "turrett". There was a second variety, halfway between what you have and what I described made ca 1780 and a little later.