For On Premises, Insane Mode uses the server extension (version 1.8.3 or greater) on both your source and destination servers. While for Office 365, Insane Mode uses Microsoft's Migration API that allows us to move huge volumes of data facilitated by your Microsoft Azure storage account.
But is my data secure?
Microsoft uses impressive encryption security. This means that even if an attacker would be able to break into Microsoft facilities to obtain your data (which in itself is highly improbable), the data itself would be unreadable. Microsoft Azure uses AES CBC 256 Standard encryption. AES encryption such a successful method that it is used by the U.S. government to protect their data. With AES encryption, both the sender and the receiver of the data must have the same key in order to decrypt and read data.
Once the migration is completed and the data has successfully been uploaded to Office 365, the only thing left to do is to delete the data associated to the migration in your Azure storage account. The steps to delete the associated data can be found here.