First, management believes only id--ts would even consider leaving ExxonMobil. Since you are considering leaving (why else would you apply to another company), you just demonstrated your “stupidity” in management’s eye.
Also, even if they would match the offer (which they almost certainly would not), you would get no raises for the next several years until you return to your reference salary.
Finally, once management convinces you to stay, thus the crisis passes, they would drop your ranking since they would now see you as not a team player and not very smart (see first point above).
My advice is to take the new job. Congrats and good luck!