Project Payment is finance department matter?
No, thats on project dept scope. If you know project management by PMI, payment included in cost area from 10 area project management. Project person should monitor and controling payment for smooth projects progress. Contractors will chase you if they have not getting payment as scheduled, and can affect on delaying project progress.
How to monitor payment?
You must know step-by step of invoicing process from site progress report untill money transfered to venddors bank account. From each process you can addressed some issue and try to fix that.
Today we have many technology to help us to do this in easiest way. There are SAP, shared outstanding payment file, and customizeed android app that we can check every time. We can put standard operation rocedure for payment on that tools. If we delay in one step of payment process more than time frame we can push to the responsible person to them by automatic notification, if no response the ntification will send to their superior. If ther a problem with invoice document, all the document should send back to contractors with required informations to fix that.