In normal usage, things are transferred from one place to another.
They transferred the load from the truck to my car.
Again in normal usage, "onto" would be used in cases where what is being stressed is the idea of lifting.
They transferred the load onto the roof of my car.
In mathematical and technical usage, "transfer onto" frequently carries the sense of being transferred to a specific place rather than a general place.
They transferred the image to a page open to everyone on the network.
This means it is somewhere on the page, but is not more specific.
They transferred the new image onto the page's old image.
This means the new image was superimposed onto a previous image. The transfer went to a specific place.