When migrating content that has DateTime values (including Created and Modified dates), the ShareGate migration tool preserves the time value itself, not necessarily the way it is displayed. This means that if the source and destination SharePoint sites are on different time zones, the displayed values will be different after the copy.
For example, when migrating a file that was modified at 1 PM from a SharePoint site that is in the PST time zone to another site in the EST time zone, the modified date will be displayed as 4 PM after the migration, which is really the same value as at the source (since there is a 3 hour difference between PST time and EST time).