I will presume you know what a coordination study is, but if you need an explanation let us know. Suppose a feeder breaker “A” on one panel provides power to a downstream panel. Suppose the downstream panel has a main breaker “B” along with a branch circuit breaker “C.” Then suppose there is a fault on the branch circuit. As a design engineer, I will not be able to tell you which breaker (A, B, or C) will open first, unless I know the model number and the settings of each breaker. That is why I would ask you (i.e., the installer) to tell me which breaker models you have installed.
My responsibilities as a designer are merely to prove that the system can be coordinated. I do that by selecting a manufacturer as my "design basis" for the equipment, by selecting specific breaker models, and finally by selecting breaker settings that will enable coordination. But after I issue the design drawings, there will be a bid process, and some GC or EC will win the bid. Their bid price will be based on equipment by a manufacturer of their choice (so long as the specifications include that manufacturer in the list of approved vendors). If by chance the one they picked is not the same as the one I used as a design basis, then my analysis will not be applicable to the particular installation. That is acceptable because the specifications include the requirement that the EC obtain from the equipment manufacturer a calculation that proves that their equipment has the required coordination.
What I am saying is essentially this: I have to prove that a solution exists, that there is at least one set of panels and breakers that can be properly coordinated. You have to prove that the installation actually works, that the panels and breakers you chose are properly coordinated.