Their POE-powered DIN-rail controllers, in your application, must be connected to Protege GX. Note that to be able to purchase and install Protege GX, you need to be certified so you will have to contact ICT USA for this.
The GX POE controllers are all single-door, DIN-rail mountable units. The are able to handle everything that is present on a single door: 2 readers (in/out on 1 door), 2 inputs (door position switch and request-to-exit detector), a relay for the door lock. Note that the 1-door POE controller does NOT support wiegand readers- the readers must be the ICT TSEC line of readers (they are RS-485 readers and both readers would communicate to the door over a single twisted-pair shielded wire; the readers use an "OSDP-style" communication format that is encrypted and supervised between the reader and the module). If you choose the DesFire TSEC reader, it will be able to read the ICT Mifare (what you mentioned) or DesFire cards. ICT encrypts the card number onto the Mifare cards using a high-security Triple DES encryption key.
Each one of these single door POE controllers is also a "site controller", allowing for the addition of up to 127 additional doors (per single door POE controller) to be connected via RS-485. In your situation, this would probably not be the case since they insist on having all-POE controllers.
You can also use each of these single-door controllers as a very powerful alarm system (more than 2000 alarm zones per controller; unlimited number of areas/partitions per controller), communicating with a monitoring station that would have their UL-approved IP receiver.
On the software side, you require Active Directory integration which is an optional licensed feature with the GX software. One caveat is that the AD integration will not pass through the access level of the user, as you request. The AD integration will create (or delete) the user issued from their HR application but the security staff will still have to assign the access rights directly in GX. A better option to AD integration is their Data Sync module which will allow the synchronization of multiple fields of HR data into the GX database. The staff at ICT USA can walk you through an integration using the optional Data Sync license.
Visitor management is handled through an integration with HID's Easy Lobby (which is a licensed feature in GX).
You will have difficulty finding a more powerful and versatile system