That is correct. Having been through the process now several months (DAF
process versus direct DIK), the church actually sends a receipt with what the donation is for. Also, there is a description line at Schwab where you can put something like, "fast offering, unit # XXXXXX, with your ward number.
However, I feel for the folks at the donations office. I wouldn't do that for a couple of hundred bucks a month. I am the finance clerk in my ward and we collect about 60X in donations than expenditures, so I don't really care if I donate it all under "tithing", even if some of it is fast offering. If I wanted it to go back to my ward, I would probably do a single donations for the entire year's fast offering to give those poor guys a break in the donation office.