A universal complaint with VWs, happens to all their models because of the spec of their rotors. Fundamentally you can't do anything about it, applying anything to the surface could affect brake pads and braking. As soon as you drive off and do some braking it'll clear.
Certainly for other models alternative rotors are available from alternative manufacturers that don't rust, but don't know if any would fit the cross, though I suspect it shares most components with the polo.
These brake disk cleaners are made only for brake dust that stucks everywhere around(tyres-brake disks-rims). If you wish to use something, use only plain white vinegar and an old toothbrush. If you do not wish to do this, just make two rounds around your house by slightly using your brakes one or two hours after washing.
All brake disc's form a slight coating of rust when left over night when the weather is damp, when you take it out first thing in the morning, and you brake the first time the pads will clean them off. you can only cure this is by fitting carbon disc's. Which is out of the realms of a T-Cross, or any other normal every day car.
As for the brake disc cleaners, it's used when you get a new set of disc's and remove the oily film they use to stop the disc's going rusty while on the shop shelves in a damp store room.
You have to be careful what you put on the disc's as you don't want to coat your pads, which in turn will affect the pads and braking distance.
You have to remember , the black on your wheel rims is mainly dust from the pads, not from the slight formation of rust first thing in the morning.