inside the record

“Her time was five seconds inside the record.”

–To me it means she broke the record by five seconds. Eg the record was 15 minutes, her time 14:55:00, that is, not outside the time of the record, just inside it. If she clocked five seconds outside the record, it would mean she ran out of its limits by the five seconds.
Do you agree?

Yes, I think your analysis is correct.