Steps to reproduce:
1. Create a request for a new task to the existing project.
2. Approve it and publish changes. Task in the project:

3. Create a new request to change the start date that is less than the current start date

4. Approve it and publish changes. Changes are in the project:

5. Create a new request to change the start date that is greater than the current start date

6. Approve it and publish changes. Changes are not in the project:

So project server does not apply changes of start date if the new date is greater than the current date.