Hi Gokulraj,
What permission mode are you using in project server 2013? Is it "project permissions mode" or "SharePoint permissions mode"?
If you are using "project permissions mode", then go to Server Settings -> Manage users and click on the user with "team member" permissions to edit.
In the next page, expand "Global Permissions" and "View Approval" permission.
It could be the issue with the categories and category level permissions.
Happy troubleshooting...
Vikram Daruru - MSFT