goutte - guzzle: Not getting file download after form submission - php

Question

I am using goutte to click a button in a form and get the download link for a file. I am correctly logged in the website.
The code I am using is what already worked in other parts of the page and gave me the right results until this point, but in this case I'm not sure it's enough:
$form = $crawler->selectButton('btn_name')->form();
$tableResults = $this->client->submit($form);
$result = $client->getResponse()->getContent(); // contains the same page of the form
The button sets some parameters and sends the request via ajax (since the page does not reload after posts):
<button id="btn_id_was_long" name="btn_name" onclick="PrimeFaces.ab({source:'btn_name'});return false;" type="submit"><span>DAE</span></button>
When I inspect the content of the response though I get the html page that contains the form but there is no trace of an attachment.
When the button is clicked with the above code I get the following headers in response:
Date: Tue, 08 Nov 2016 16:37:42 GMT
Server: Apache/2.2.29 (Unix) mod_ssl/2.2.29 OpenSSL/1.0.1e-fips DAV/2 mod_jk/1.2.31
X-Content-Type-Options: nosniff
X-Frame-Options: SAMEORIGIN
X-XSS-Protection: 1
Liferay-Portal: Liferay Portal Enterprise Edition 6.2.10 EE GA1 (Newton / Build 6210 / November 1, 2013)
X-JAVAX-PORTLET-FACES-NAMESPACED-RESPONSE: true X-Powered-By: JSP/2.2
Transfer-Encoding: chunked Content-Type: text/html;charset=UTF-8
When I perform the same action in the browser I get this instead, with the file download:
HTTP/1.1 200 OK
Date: Tue, 08 Nov 2016 17:31:34 GMT
Server: Apache/2.2.29 (Unix) mod_ssl/2.2.29 OpenSSL/1.0.1e-fips DAV/2 mod_jk/1.2.31
x-content-type-options: nosniff
x-frame-options: SAMEORIGIN
X-XSS-Protection: 1
Content-Encoding: gzip
Liferay-Portal: Liferay Portal Enterprise Edition 6.2.10 EE GA1 (Newton / Build 6210 / November 1, 2013)
Content-Disposition: attachment;filename=DAE_00001_17/10/2016.pdf
Expires: 0
Pragma: public
Cache-Control: must-revalidate, post-check=0, pre-check=0 portlet.http-status-code: 200
Keep-Alive: timeout=5, max=99
Connection: Keep-Alive
Transfer-Encoding: chunked
Content-Type: application/pdf;charset=UTF-8
Any clue what I'm doing wrong?