I don't have quartzite so sorry if this is off-base, but what you're describing (especially knowing it's caused by oil) sounds like etching to me??

so frustrating that pieces from the same slab respond diferently. Sorry you're dealing with this!

Have you called your fabricator to come and reseal it? Obviously the sealant didn't take evenly - I think they need to come and take a look.

Agree with mayberry. Your fabricator/counter company should be interested in this issue and helping to resolve it. Did they say anything other than it was sealed? It does sound like more sealer is needed.

I have a lot of White Macaubas in my 2 month old kitchen. The fabricator applied a standard dupont sealer prior to installation. After installation, and at the recommendation of my stone person, I applied DuPont's Stonetech Bulletproof on my White Macaubas. It was hard to find, expensive, and labor intensive to apply, but I am so glad I did. As I applied the sealer (in small sections per instructions), some areas would become very grey while other areas did not look any different. I thought I ruined my stone and had a little freak-out moment before I figured out what was happening! The very grey areas were the areas that had not been adequately sealed by the fabricator. I could see lines where the original sealer had been wiped on/off. The "grey" areas were where the new (Bulletproof) sealer had soaked in, and these areas dried back to the original color within an hour or so. The "grey" areas that had not been adequately sealed originally were in random areas . Maybe you have some areas that were missed during the original sealing process as well? Water, oil, lemon, wine, etc., all cleans up fine. The stone does, so far, seem to be bulletproof. If we had not had the post-installation sealer application, I'm sure we would be having problems because there were too many unprotected areas on the stone!

Each slab should be tested for porosity. It is quite simple , just place a palmsized or smaller puddle of water.
Let it sit for 10 minutes or so. Then wipe away with a paper towel. If you are left with a dark mark you just confirmed your material is porous. The longer the spot takes to dry out gives you an idea just how porous the material is.
Then it is your decision to hire someone or do it yourself.
In your case Heidia you need to remove the stains first.
Something you should have your fabricator take care of for you.
He should reseal the surfaces.
You should be aware of what he uses and should leave you some.
You should do the water test 24 hours or more after sealing.
The reason is sealer takes time to cure and you will get a truer result after a day or more.
If you still get a wet spot from water it needs additional applications. I use the word applications because when we seal one application will usually be more than one coat.
Test a day or so after each application for results.
While I consider sealing a professional task I think it can be done better by a homeowner. The reasons are quite obvious as the many posts written on garden web regarding insufficient sealing of new stone.
Homeowners will always be there to test and if needed apply additional applications. Like ott2 stated the sealer could be seen penetrating the surface. When the surface dries back to normal repeat the process. Again when I seal a countertop that is porous I try to get as much sealer into the surface as possible. Again one application to me can be many coats but still one application. Then test after the cure. You will notice a major change in the absorption rate.
Very important point-if you test your unsealed stone and it isn't porous and absorbed nothing do you need to seal?
Chances are that your stone is very dense and will not stain.
My opinion is it doesn't need sealer.
However we are flooded with sealer marketing and hype so for some folks they wont be able to sleep if their non porous surfaces aren't sealed. If this is the case just make sure that all the sealer residue is removed from the surface of the stone. If not it is possible to encounter other issues caused by the sealer residue.
Also I am always asked about how often people should seal. Easy answer-use a neutral PH cleaner that will clean your surface but not degrade the sealer. The water test will always tell you when surfaces become porous.
Sealers will last if maintained properly for years.
Most sealer companies market sustained sealing capabilities but then somehow have folks thinking they need to seal every six months to a year.
Always keep in mind the actual performances of an impregnating sealer.
"to temporarily inhibit the intrusion of staining agents from the surface of the stone"
End of list of performances of an impregnating sealer.
One other important note-use a sealer that will protect against oil based and water based stains.
Hope this helps.