"For other areas, you must use a TDMA or CDMA phone. (old systems that only works in America. )"
This is not correct.
The most widely available cell phone service in the DR is for 800 Mhz AMPS cellulars, aka, analog (Advanced Mobile Phone Service). Many CDMA (digital) and TDMA (digital) phones also support 800 Mhz AMPS, however be aware that many require special programming to be able to select between the "A" (Tricom) or "B" (Codetel) carrier (see www.BocaChicaBeach.net/staying_in_touch.html for a discussion).
AMPS is also a de facto standard throughout Mexico, Central and South America, very common in the Pacific Rim and also found in Africa and the remains of the USSR. Today, about half the cellular phones in the world operate according to AMPS standards, which, since 1988, have been maintained and developed by the Telecommunications Industry Association (TIA). In summary, AMPS is on every continent except Europe and Antarctica.