Nothing to be confused about. If you want to work legally in the DR you will need residency. Not sure what your place of employment needs so you should maybe ask them.
It costs from 1000 to 1500 US dollars if done by a lawyer. I would not suggest doing the paper work yourself unless you know Spanish well.
Some info
Read all of it here
DR1 - Legal
Residency Advantages
What are the advantages to getting a residency?
A resident can work and do business in the Dominican Republic; a non resident cannot do so legally.
Being a resident facilitates a number of business transactions in the DR, including obtaining bank loans and applying for credit.
A resident does not have to post a bond (usually quite high) in court when he decides to sue in the Dominican Republic; a nonresident is required to do so.
A resident can enter the Dominican Republic without having to buy a tourist card; a nonresident must obtain a visa or buy a tourist card.
In case of inheritance, a non-resident beneficiary must pay a 50% surcharge on estate taxes; this surcharge is not applicable to the resident.
A resident is allowed to bring in tax free his household items, ranging from kitchen appliances, to furniture. Article 13 of Law #146-00 expressly exempts from any duty the importation of the personal effects and household goods of foreigners immigrating into the Dominican Republic and of Dominicans coming back home to live permanently after residing abroad for more than two consecutive years. And Law 168 grants a discount that ranges from 20% for one year in your name to 60% for five years on vehicles that will be imported together with your household goods.
A resident does not need to purchase a return ticket when traveling to the DR.
You will be able to get a valid Dominican driver's license so that your insurance plan will cover you if you are involved in a traffic accident. Foreign driver's licenses are only valid for the first 90 days. Otherwise, to keep your foreign driver's license valid, you will need to exit the country before the 91st day to start the 90 day count over.
Disadvantages:
A resident is subject to income tax on worldwide income from investments abroad after the third year of residency in the country. However, this applies only to income from financial investments, not to income from other sources such as personal work. Of course, the resident will also pay income tax on Dominican income.