Your contractor should pull the permit. Here is what is actually happening while they do.
When a permit is required
The City of Evanston requires a building permit for any roofing work valued over $1,000. That covers essentially every replacement and most non-trivial repairs. Permits are typically issued in 5–10 business days for standard work.
Documents the city requires
Contractor information, proof of insurance, scope of work, and approximate value. For landmark-district properties, the Certificate of Appropriateness must be in hand before the building permit will be issued.
The mid-project inspection
Cities the size of Evanston do not generally inspect every roof mid-tear-off, but they reserve the right. Your contractor coordinates any requested inspection, and photo documentation usually stands in where a physical inspection is impractical — which is one more reason to start with a documented roof inspection.
Final inspection and close-out
The city issues a Certificate of Completion after the work is invoiced and any required inspection passes. Ask for the closed permit number for your records and keep it with your home documentation — it surfaces at resale. On a landmark or historic-district property, the review that precedes all of this is covered in roofing options for historic Evanston homes; if the work turns out to be a single slope or flashing detail, a roof repair may be the whole permit.