An RCD detects a fault between live and earth, neutral and earth, and thus trips, saving you from a shock, an mcb detects faults between neutral and live and thus trips, saving you're cable from burning out, Rcd's have minutely different sensitivities to tripping (manufacturers etc) but will trip in enough time to prevent you from serious electric shock. If you have a dual rcd board and the Dyson causes only one RCD to trip but not another then I'd get the RCD checked out too (we have passable trip limits based on testing, and they do fail quite often).
I'd say the machine has a dead short on it somewhere and will require further investigation.