When you change the project rate or task-based rates, the new rates will be applied to all past time logs, unless they have been locked, invoiced, or approved.
If you need to apply the new rate after a certain date, the best option would be to approve all existing time logs on a project before changing the rate. Here's how to do this:
Go to the Detailed view and filter out all time logs for the project/task.
Then add the 'Approval status' column to the view with the 'Settings' button (please see the screenshot below). Next, select all logs and click 'Approve'.
Once time logs are approved they will keep the old rate and will not be updated with the new rate.
After you have approved all existing time logs, change the billable rate for the project (or task). This way the new rate will only apply to future time logs.
If you need to apply the change after a certain date in the past, approve just the time logs up to that date. The logs that are not approved will be updated with the new rate.