The Server/Data Center version of Epic Time stores information and displays it via the custom fields.
The Cloud version of the app doesn't store information and retrieve it via on-the-fly calculations when a user opens an issue / gets the report. That is why you do not need to migrate the values of the Epic Time custom fields while migrating on Cloud: just add the app to your Jira and get the Epic Time values in the relevant sections.
Note that unlike the on-premise version the Cloud version will not allow you to use the Epic Time information anywhere else: as a column in Issue Navigator, in standard Jira reports, etc.
