The first problem that you will face is not Ca. DV, but your immigration status. Department of Homeland Security has access to all of your records no matter what state. When they have a report of DOJ, that conviction will come up. Therefore, talk to your attorney and review other options available than pleading guilty to refusal.
States have computers, so there is an excellent chance that a conviction in NJ will attach to your California Drivers License in about 15 minutes. Refusal is an automatic suspension of your license. I think you have a bigger problem than you realize.
I represent Employers, but I can recommend Worker Attorneys in So Cal if you ask.
Aside from your DUI, you should also consult with an immigration attorney before you resolve your criminal case to see how this may impact your visa. Best of luck.
This is not intended as legal advice. No attorney / client relationship exists because of this response.
Tell your NJ attorney to pick up his phone and call an experienced CA criminal defense attorney. You may also want to consult with an immigration attorney.
Law Offices of David Shapiro 3555 4th Avenue San Diego, CA 92103 (619) 295-3555
Your biggest issue would appear to be your immigration status. For a knowledgeable answer on that you're going to need a knowledgeable immigration lawyer.
As for the refusal (and if it occurs, the DWI) - yes, CA will be notified almost as soon as the conviction(s) are entered in New Jersey. Under the interstate Drivers Licence Compact (CVC Sec. 15000), the violation(s) will be reported over, and then the CA DMV will begin to act.