Hello Jordan,
I'm afraid, it is not possible to get client reports using the Manager accounts customer Id. You will need to specify the client customer Id of the client account in the
request header when downloading reports. If you need to gather reporting data for multiple accounts, you will have to submit a separate report request for each account by setting the clientCustomerId as mentioned
here.
Additionally, you could download AdWords reports for all accounts directly under your manager account using the
Parallel Report Download. You can also refer to the code samples in other languages available
here.
Regards,
Bharani, AdWords API Team.