iPhone 4S Swisscom official unlock problem

So, just recently Swiss carrier Swisscom has announced that ALL iPhones tethered to this operator are to be unlocked starting from 1st of July. It's all simple - just connect your phone and synchronize via iTunes - and it instantly gets unlocked, but...

I met some problems even doing such a "simple" task.

At first, I restored my iPhone. Then I plugged in a new sim-card (as Swisscom proposed me to do) but I stuck on the activation, during which it says this:

"The sim that you currently have installed in this iPhone is from a carrier that is not supported under the activation policy that is currently assigned by the activation server. This is not a hardware issue with the iPhone.Please insert another SIM card from a supported carrier or request that this iPhone be unlocked by your carrier. Please contact Apple for more information."

And I do not have an original Swisscom sim-card. But should I? The carrier itself advises me to insert the NEW one. Something wrong here, I guess.

I have iPhone 4S black, 32 GB, 5.1.1 firmware (no jailbreaks and no other modifications).

I'm pretty new to the process of unlocking the iPhone as I'm doing it for the first time. (plus I'm not quite sure that I asked the question in the right place, hehe)

So...

Could you please advise me WHAT SHOULD I DO NOW?