Most of the time records during a day are adjacent - they go one after another. If a user needs to adjust the start time of a record they most probably will need to change the end time for the previous record. Similarly, if the end time for a record needs to be changed the start time for the next record needs to be changed accordingly.
I would suggest adding an “adjacent” icon as a checkbox on the time record line next to the time edit boxes. If a user changes the start or the end time for a record they might tick this check box and the end or the start time of the next/previous record would be adjusted accordingly.