Dates being exported outside of the specified date range is likely due to the fact that the Job Start Date and/or Job End Date is being exported instead of the Job Segment Date.
To illustrate, let's use a 5-day job that starts March 1st and end March 5th. The Job Start Date will always be March 1st, the Job End Date will always be March 5th and the Job Segment Date will be each of the dates of the job 1 per row.
The above solution is for the Job Segment Report Type only and should not arise if you are exporting a Jobs Report Type.
To learn more about Jobs Reports and Job Segments Reports see What is a Custom Jobs Report vs. a Custom Job Segments Report?