No complicated maths, both glasses have the same amount of wine in them, 1 tumbler removed from glass one and then replaced, therefore each has as much of the other colour in it. If one had more than the other it would have gained some volume. Ratio makes no difference as far as I can see.
See, that's my point.
Take a tumbler of red and poor it into the white. This means you've pored a tumbler full of 100% red into the whit glass.
Now, you have a pink "Rose" white wine glass. Yes? So there MUST be some red in the tumbler when returning the same amount of fluid from the white glass to the red.
Therefor there MUST be more red wine in the white glass than there is white wine in the red glass.
Yes the total volume is the same, but that is NOT the question. That being, after pooring a tumbler of red into the white, THEN poring a tumbler from the white(pink) back to the red, is the more red in the white, or more white in the red...?
Just to repeat, they said the answer was, as you say, the same. Same total volume yes. But not the same ratio. Proof being in the colour.