Whose job is it typically to create the flow schematics for monitor basins? ADS or the Client?

It varies. Ideally, this task should be performed during the initial planning stages of an I/I study. From a practical standpoint, whoever has control of the GIS data should be the one to perform this important task. The municipality often has the best access to the GIS data and is best positioned to correct any GIS errors identified in the process. However, from a contractual standpoint, this task is sometimes assigned to a consulting engineer or to a flow service provider.