How do DR surgeons make the waist smaller (snatched) than doctors do in the States?

It is the technique, expertise and skills that will get the best result in shaping and slimming the waist. For best results, I recommend a hi definition procedure like VASER liposuction. I use VASER HI DEF with ThermRF and fat grafting to get the most fat removal, skin tightening, contour and definition. This combination will give you the most toned result. I recommend getting a formal evaluation with a hi definition physique expert. Best, Dr. Emer

Snatched is a term that I have recently heard in my office. While the term is new the goals of the liposculpting and Brazilian Butt Lift are not.  The vast majority of my patients want to have have a tiny (snatched) waist and a perkier, more full butt and hips.
In the Brazilian Butt Lift the combination of the liposculpting and fat transfer is what leads to the figure transformation.  In this transformation my patients can go from square to an hourglass figure.  The smaller the waist the better the hips and butt will appear. 

The snatched waist comes from the liposuction.  I turn all my patients on each side.  This gives me direct access to the love handles as this key in terms of making the waist as small as possible.  This liposculpting will not only make the waist tiny it will give us good fat that we can use to fill the hip dip and butt.  This combination will give patients more of the “s” curve that they desire for their overall shape.

The first step in a Brazilian Butt Lift (BBL) is the liposuction.  I think people often forget how import this part is in making the overall figure as sexy as possible.  The liposuction during a BBL is not only for harvesting fat to fill the hip dips and butt, it is used to shape and sculpt the waist.  The are of a Brazilian Butt Lift is in the combination of the liposculpting and the butt enhancement with he fat transfer.

Please discuss your Brazilian Butt Lift with your Board-Certified Plastic Surgeon so that they can discuss the surgery and the results that are possible from the procedure.  

I think there are excellent surgeons abroad and stateside; and, there are some not-so-excellent surgeons in both locations, too. I have not specifically seen tighter/smaller waists in patients treated in the Dominican Republic as compared to the United States. Different surgeons will get different results on different people. So, because one person may look really small-waisted postoperatively, this doesn't mean that another person with a different frame will be able to achieve the same result with the same surgeon. 
I have seen and taken care of many patients who have had cosmetic surgery in Central America who have had challenging complications. That being said, I'm sure I don't see the ones who have no problems. However, if something unanticipated does happen, having your surgeon 1 or 2 airline flights away would likely be prohibitive to getting timely care. 
Best of luck!