AT&T has more monetary and marketing muscle than practically anyone else on the planet? The point is that mag tape will be more recognized as a storage medium than IOTL, since AT&T--you know, one of the biggest corporations on the planet?--is pushing it, or at least selling it. It's pretty likely that at least some of the scientists working on the first computers would be from AT&T or know AT&T people...
EDIT: Also, it's not strictly true that mag tape was invented prior to this. What we think of as "mag tape" was only invented in 1928--in Germany. Understandably, this was actually pretty secret until the end of the war, and American technology was behind. The other form of tape that they had was much less advanced and wouldn't have been useful for tape data storage (too heavy and too much was needed), but further AT&T investment might have lead to the development of oxide tape, which would have been much more useful.
Yup, there's no efficient tape recording systems outside of the Reich before the end of WWII. That's why there was no standard technology, with instead a cacophony of sound coming from wire recorders, blattnerphones and old-fashioned wax discs being used throughout the Western communications industries.
The ting is that it did not need to be a answering machine. They could have sold it as recording device to radio stations
Not only is this the most obvious first use for magnetic tape (as opposed to data storage for computers yet to be built, or replacing office workers) but it leads directly to another truly revolutionary application IMO--early Television.
I think it's a certainty that some kind of video tape, somewhere in the range between OTL's VERA and Ampex's 2-inch tape, will be developed by the end of the Second World War. The request for playback machines utilising this miraculous, flexible magnetic tape is inevitable, what with cathode ray displays being used for radar from the very beginning of the war, and the USAAF actually employing TV cameras in their early 'smart bombs'. (Of course you can ask the question, "why would the WAllies create video tape for their radar and smart bomb tech when Germany didn't do that IOTL?" To which I can only respond, "Lendlease, Manhattan Project, no confusing Wanderwaffe administrative decision making, mo money, etc".)
Imagine if selected events from the last year or two of the war were captured on b&w tape in the same way the Kennedy/Nixon debates can be seen today. FDR making his last address to congress, Doenitz surrendering to Montgomey at Luneberg Heath, kamikazes attacking the US fleet carriers off Okinawa. The mind boggles at having bits of the war preserved that way, particularly if the signals corps or whoever ask to be able to use colour TV technology.
The postwar effect will be pretty enormous. Kinescope technology isn't even invented until 1947; having commercially available video recording
before this happens will advance the business model of the US networks by several years. Of course Kinescope itself may be advanced by several years if the WAllied military are using CCTV for many more different purposes than they did in our timeline.
IMO this is all before we even get to the institutions who were operating the early computers realising, "Hey, we can create an electronic library full of every single little calculation we ever want to run through our machine!"