存在PHP数组键

I'm working with an API and now i want to check if an array key exists then do something.

With an array i gather data like this:

$pers_payload = array(
    'gender' => 'Unknown', //or Male / Female
    'first_name' => $_POST['billing_first_name'],
    'family_name'   => $_POST ['billing_last_name'],
    'email' => $_POST['billing_email'],
    'linked_as_contact_to_organization' => array(
        array(
            'organization_id' => $organization_id, // add the person as a contact to the newly created organization
            'work_email' => $_POST['billing_email'],
            'work_phone' => $_POST['billing_phone']
            )
        ),
    'visiting_address' => array(
        'country_code'          =>  'NL'
        ), // can be extented with other address data
    'postal_address' => array(
        'country_code'      =>  $_POST['billing_country'] 
    )   // can be extented with other address data
);

Then i use a get request like this:

$tet = $SimplicateApi->makeApiCall('GET','/crm/person?q[first_name]=Kevin');

And then i check if the array exists inside the results of the get request like this:

if(array_key_exists('first_name', $tet)) {
   // do Nothing
}else{
   // make API call
   $person = $SimplicateApi->makeApiCall('POST','/crm/person',json_encode($pers_payload));
}

Im sure the get request is working, because i did a var_dump($tet); and i got this result:

  array(3) { ["data"]=> array(6) { [0]=> array(18) { ["id"]=> string(39) "person:71cf33fb785433ab66550e5701120079

Well thats part of what i got, i cant post all of it. because it contains sensitive information.

For some reason even if the array_key exists this code still runs:

$person = $SimplicateApi->makeApiCall('POST','/crm/person',json_encode($pers_payload));

--

array(3) { ["value"]=> bool(false) ["id"]=> string(41) "interest:7d3458131ea89afbe1bb3149bee8b668" ["name"]=> string(3) "Web" } } } } ["gender"]=> string(7) "Unknown" ["first_name"]=> string(5) "Kevin" ["family_name"]=> string(7) "A" ["full_name"]=> string(13) "Kevin A" ["email"]=> string(24) "ma@edd-marketingsuppxort.nl" ["phone"]=> string(8) "06269684" } [5]=> array(11) { ["id"]=> string(39) "person:51045f230a9cc39136aaf3a22a069eb0" ["interests"]=> array(1) { [0]=> 

What are the first array keys of $tet?
We can see the first one is data, but what about the others one?

if(array_key_exists('first_name', $tet['data'])) {
  //code...
}

edit: as @lma says array_key_exists can not dig into child, and even the edited structure you gave us look weird, some trailing } in the middle of the array.