That's a remarkable phenomenon.
My guess is that your steam cleaning left a droplet of condensation/spray at the centre of each circular mark. This then soaked into the slightly porous ceiling and then spread out transporting stain from the plasterboard outwards and depositing it at the point the water evaporated. 'Coffee mug stains' form in a similar manner.
I'd deal with it by waiting to make sure it's dry, which could take a several months, then slap on a layer of 'one coat stain stop', and then repaint the ceiling.