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When arriving in the US, the passport control gave me an "Admitted" stamp with class "WT until 04 may 2017". However I have a (J-1) visa until June.

Can this become a problem, or is the stamp unimportant as long as I have the visa?

Update: I emailed the cbphoui94@cbp.dhs.gov address from the 'DEFERRED INSPECTION SITES' list. They asked me for

1. Copy of the Passport biographical page


2. Copy of the United States Visa


3. Copy of the Admission stamp in your passport


4. Boarding pass or flight information


5. Address in the United States


6. Copy of your DS 2019

I sent that to them, and today they replied that

After further review, our records indicate that you were admitted properly. This was not an error, therefore no correction can be made.

I'm not sure if they mean that I was actually J1 admitted, or that admitting me with WB status was the proper thing to do.
The i94.cbp.dhs.gov/I94/ website still tells me that my status is WB and I have to exit in May.
I have written back for clarifications, so that is all very exciting.

Update 2: I received the following clarification:

The class of admission and admit until date indicated on your
electronic I-94 record is correct.

You presented yourself as a
Visa Waiver Program applicant and utilized the Automated Passport
Control kiosk on your last entry into the United States.

I suppose this means, that the admission is not considered 'a mistake' on the part of the inspection site, and thus it cannot be corrected.

I wonder if there is a better word to use. For now I have replied if they can help me with "changing" i94 status.

Update 3: Houston never replied to my last email, but I got in contact with my host organization (University of Texas), which perhaps is where my focus should have been from the beginning. The University called up Austin-Bergstrom Airport and arranged for me to see an officer there. The officer quickly changed my status and gave me a new stamp. But! Paranoid as I have learned to be, I checked the electronical i94 record, and it wrongly still had "Admitted until may" rather than (as in the stamp) "Status until D/s". So I went back to the officer and she corrected it again.

Thus, I believe everything to be good now, but I'll still see the international office of the University again this afternoon, so they can double check.

I'll probably take away the following lessons: Don't use the kiosk if you have a visa; Don't trust anything before you have found wifi in the airport and checked your i94; Get in contact with your host organization; and Stack Exchange is great. Thanks everyone!

Check here what admission class you got (WT or J1). If it says J1, don't worry - the electronic record is superior to the passport stamp.

If it says WT, however, you must get it fixed immediately by going to a deferred inspection site, a list of which can be found here. Otherwise, as soon as you start performing your J1 activity, you've broken immigration law and will be deported if caught.

UPDATE: Given the reply you got:

The class of admission and admit until date indicated on your electronic I-94 record is correct.

You presented yourself as a Visa Waiver Program applicant and utilized the Automated Passport Control kiosk on your last entry into the United States.

You were admitted in WB status (unsurprisignly, because the electronic record invariably contains the correct info) because you probably presented your passport open at the main ID page (after using the kiosk, which is not for J1 visa holders) and didn't present your DS-2019.

WB/WT status cannot be converted to any other status

Unless the CBP make an exception and agree to correct it, you'll have to leave the US (Canada and Mexico are fine), and re-enter, asking to be admitted in J1 status. Present the passport open at the visa page as well as your DS-2019.

Bear in mind, if entering from Canada or Mexico by land, a white form will be stapled into your passport (ask immigration to create an electronic I-94 as well in case you lose the white form - at major crossings they're usually able to). Keep this during your whole stay in the US, and hand it in at the check-in desk when it's time to go home.

It is important what status you were admitted in, regardless of what valid visas you have in your passport. This becomes vital IF you are apprehended for some reason or accused of violating status or maybe need to extend duration of stay.

Being admitted under VWP gives you fewer immigration rights if something happens. You forfeit the right to an immigration judge if something happens and they decide to deport you. Also it is annotated in your immigration record.

What should I do if I was admitted incorrectly to the United States?

If you were admitted incorrectly to the United States, you should
visit a local Customs and Border Protection (CBP) Deferred Inspection
Site or Port of Entry (POE) that has a Deferred Inspection office to
have his or her admission corrected. See list of Deferred Inspection
Site locations and list of Port of Entry locations.