When the user's name in MS Project is set as Last Name, First Name and in Web TimeSheet, the name is set as First Name, Last Name. Data transfer from MS Project to Web TimeSheet would not synchronise with the users in Web TimeSheet, because the integration manager would consider the users in Web TimeSheet as different users.

In MSP Integration manager, go to the "Resource Mapping" tab. 
In the Resource Name Formula change $FirstName $LastName to $LastName $FirstName. This allows the application to flip the name and transfer the user data.