I'm only on my first Tru-Oiled kit, but it was noticeable that even after using the Tru-Oil sealer, the Tru-Oil itself was picking up stain from the top which was visible in runs over the binding. I am only using a single colour, so it had no real impact on me.

The oil itself is a solvent so any stain pigment is likely to be partially absorbed by the oil and redistributed as you rub it.

I suppose you have to be prepared for this with the first couple of applications and with a burst 1) work from the centre out to the sides, so that you are moving a lighter pigment over a darker one 2) use a new part of your cloth each time you add more oil so you don't rub darkened oil into a light area and 3) don't rub it it hard - apply to the surface, wipe it on (centre to edge) and leave it be.

Thinking about it, although it doesn't seem a natural thing to do, you'd probably be best leaving small gaps between each wipe, so that you aren't dragging TO that has had a chance to absorb some stain over the rest of the body and blending it together. Then once the TO is dry, then go back and wipe oil in-between the gaps only. Maybe repeat this a couple of times before you start doing the whole body. Once there are a couple of coats on, you shouldn't get any significant colour leaching.