Because that is what all the shift register displays say they contain.
Actually the Ebay adverts do not seem to mention the controller.
I have followed Forum conversations from library developers e.g.Bodmer, SteveStrong, ...
They all say ILI9486. All schematics say ILI9486.
The best thing is to just try Bodmer's ILI9486 initialisation.
Then do some diagnostics to verify the exact controller model.
The shift register displays are write-only. However there are slight differences between ILI9481, ILI9486, R61581, RM68140, ...
I can post a sketch that shows the differences.
I have never owned this type of display. But I would just follow Bodmer's advice. He shows the wiring. I have suggested the defines.
Just try it.
David.