If your car is under the full warranty then that is a resounding NO...you do NOT have to pay for that...!
And of course of all things though, that would be one of the very least of things in the category of which NOT to be paying for. Be sure that they know this and if I were you, I would be deferring your future ALFA issue to another dealership. This would be something I would be pointing out to them as well albeit in a very friendly and positive manner so as not to burn any bridges just in case.
More to the point, I would also recommend that you contact ARUK and detail to them as to what is transpiring while gaining their assurances that this will not be the standard practice in the future.