The document you are referring to is called a Request for Technical Proposal. Back before the feasibility study began, Copper Fox would likely have sent Tetra Tech an RFTP. This RFTP would outline items such as the scope of work, the deliverables, the timeframe, milestones, and progress tracking. Tetra Tech would respond by submitting that info as well as resumes, proposed subcontractors, an execution plan, a manpower estimate, and a budget.

The budget would be based on an assumption of hours worked. If the cost comes in below budget, then there is a partial credit back to Copper Fox. If the cost is over budget, a small discount was likely offered on those extra charges.

A similar approach was likely taken on the schedule. A small bonus was likely on the table if they finished ahead of schedule. I don't believe there is typically any penalties for being behind schedule other than the discounted overbudget rates.

At least this is how I've seen things done.