I find this story odd because IBM was consistent with their keyboard nomenclature across multiple products, and the 3270 series mainframe terminals used the Tab key, located in the same place where you would find a tab key on a modern keyboard, to move the cursor to the next field.
As an aside, it's worth noting that moving between fields was important enough on IBM terminals that they had a dedicated "back tab" key located on the opposite end of the keyboard to the tab key. On the original IBM PC, they decided to combine both functions into a single key. As a result, the tab key on the classic PC keyboard features the symbols for both forwards tab and back tab on the same key, the back tab symbol being on top to indicate that you need to hold down shift to use that function.
EDIT: The 5250 series terminals used the terms "Field Advance" and "Field Backspace" instead of Tab and Back Tab, but otherwise they used the same symbol on the keys, and the keys were located in roughly the same position as the 3270 series. Reference: https://www.bitsavers.org/pdf/ibm/5291/GA21-9409-0_5291_Disp...
https://www.bitsavers.org/pdf/ibm/3278/GA27-2890-4_3278_Disp... (Page 73 of the PDF)
As an aside, it's worth noting that moving between fields was important enough on IBM terminals that they had a dedicated "back tab" key located on the opposite end of the keyboard to the tab key. On the original IBM PC, they decided to combine both functions into a single key. As a result, the tab key on the classic PC keyboard features the symbols for both forwards tab and back tab on the same key, the back tab symbol being on top to indicate that you need to hold down shift to use that function.
EDIT: The 5250 series terminals used the terms "Field Advance" and "Field Backspace" instead of Tab and Back Tab, but otherwise they used the same symbol on the keys, and the keys were located in roughly the same position as the 3270 series. Reference: https://www.bitsavers.org/pdf/ibm/5291/GA21-9409-0_5291_Disp...