First, congratulations for doing propper due diligence and coming to this website to learn about whatever your curiosity brought you here.
Second, don't accept that offer. Just don't. Move on and look for something else. Regardless of yoru circumstances or how great it feel to finally getting an offer, drop it and move on.
ExxonMobil will not only destroy your career and make you less employable every day you spend, but it will also mutilate your SOUL.
You will come to hate your job at exxon with every fiber of your spirit, and you will meet cynism, disengagement, brown-nosing, back-stabbing, and low morale like nowhere else.
Also, if you are a foreign national looking for a green card, you'd better think twice. It's a trap, believe me, you will be better off returning to your home country, as the price you will be paying to gain permanent residence is to work in a prison like totalitarian regime that will abuse your talent and insult your intellect.