How are the system development and integration procedure separated for Integrated Modular Avionics?
The Aircraft System Manufacturer is the company developing the system that is being implemented on IMA hardware (supplied by the Avionic Module Supplier). They will likely develop software to load onto the IMA hardware to perform certain functions.

For example:
Airbus would like to implement a Thrust Reverser Control System for their new airplane. The system would take in some parameters gathered from various sensors within the aircraft, perform the necessary logic and/or calculations, and then provide the necessary control commands to the thrust reversers.

Now Airbus doesn't want to develop this specific system, so they contract it out to another company ACME Avionics. They provide ACME with the System Requirements Data, which describes how the system must operate, what inputs it will use, the Design Assurance Level of the system, and the IMA modules the system must use to implement the requirements.