Storage Gateway - Virtual Tape Library *direct* archive to S3 Glacier Deep?

A customer who is studying the possibility of using Tape Storage Gateway. They have asked for a 120 TB/month write costs estimation. From the FAQs:

Q: What Amazon S3 storage classes does Tape Gateway support?
A: Tape Gateway supports S3 Standard, S3 Glacier, and S3 Glacier Deep Archive storage classes. Data on your virtual tapes is stored in virtual tape library in Amazon S3 when backup application is writing data to tapes. After you eject tapes from backup application, your tapes are archived to S3 Glacier or S3 Glacier Deep Archive.

I understand the data is stored in the S3 virtual tape library and then moved to Glacier Deep Archive (in my case).

What's the correct approach?