When migrating settings and/or data from a Project Server + Project Financial Server test environment to a production environment, you always have to make sure you have the correct settings for the domain accounts used by different processes.
In order for the workflow configured with financial settings to work, check the following:
1. The Project Financial Server Queue Service should have the same identity as the Sharepoint Timer
2. The Workflow Proxy account must have the following minimum permissions:
Category permissions (My Organization):