How are categories migrated?
Categories and associated colors are a mailbox configuration setting, and therefore are not migrated. However, if an item in the Source has a category assigned, it will show at the Destination as having that category assigned even though the category will not be listed under "All Categories" in Outlook.
You must manually recreate the categories at the Destination. Once a category is recreated and a color is assigned, all Destination items with that category will update to show the new color. This can be done either before or after the migration is performed.