First of all, Dominican salons aren't all created equal, but at their best they are excellent! They can handle most textures because they have a wide array of textures within their ethnicity, however straight hair is their goal so most likely they will push for a relaxer. In Latin American culture the hair ideal is long, shiny/silky hair with swing. A lot of Dominican woman have hair textured similar to many of us so they've perfected achieving the straight and bouncy hair without the flat irons and heat (particularly detrimental to fragile black hair). Part of the reason for their popularity is that they provided black women with results that were seen (at the time) as only attainable by straight haired women.
Their approach to hair care probably goes against many of the things our moms would have done, no grease, very little leave in, a little shine serum, but heavy on the deep conditioners and home recipes. A good Dominican salon tends to focus on hair care as much as the styling.
Their rollersets alone yield shiny, straight hair. I get my roots blown out and I'm done. Dominican stylist use the blow dryer like a second hand so be careful, too much and you're in for major breakage. It's 2yrs and I've just now perfected the same rollerset at home.
Lastly, price. The good ones can offer the results you would expect from a high end salon for $15/$20 for a wash, set and blow dry. Like anything, moderation is key and not all salons are equal. As with any trend you have a lot of Dominican salons opening up and sometimes it's by ppl that know nothing about hair or don't have any respect for clients. So beware of salons where they rush you in and out or are rough with your hair.