'Contains FCC ID' compare to just 'FCC'. Certificate of conformity
If your device has been fully tested to comply with FCC then you will be given an FCC ID.  This is the ID for your device.

It sounds like your device is only going to be partially tested, and that the majority of the testing will be taken as read by using the previous test of the WiFi module.  The WiFi portion of the device will not be tested.

I would guess that you are being told to put the ID of the WiFi module on the product for public inspection.  This will be so that the test for the WiFi can be obtained and read if required, as well as the test for your device.