Has the employer asked you to get your residency? If you need it before you start then you will need to wait 3 to 6 months - that is how long it will take.
If the employer does not ask you to have it first - go ahead and work. For you it is not a problem. For the employer it can be. Dominican labor law is territorial in nature. All who work here in the country are covered by the labor code. So you are covered.
If you want to know about residencia do a search to find out the process and what you need to prepare.
