For that reason I don't seem to succeed getting the table and all I get is the buttons at the top of that page.
Any suggestions or ideas on how to solve this?
cURL will only get you the markup of the page. It won't load any additional resources or process the page. You probably want to look at something like PhantomJS for this. PhantomJS is a headless WebKit browser. It has its own API that lets you "script" behavior. So you can tell PhantomJS to load the page and dump out the data you need.
Depending on what exactly you're trying to do, you could just fetch the JSON data that makes the table:
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