Unsure but if they didn't it was up to them as they (CFS) have to book in with Adelaide fire on 093 dont they? So MFS would have known about the call?
A better way would be to ask Adelaide Fire to respond the appropriate MFS resources as soon you receive page - thereby trying to adhere to the EMA agreement as much as possible (Under that agreement the response must be a Dual, SIMULTANEOUS response by both CFS AND MFS). If a brigade runs a Duty Officer system then this could be their responsibility.
Alternatively do it when you acknowledge the page.
I wouldn't consider advising Adelaide Fire that you are mobile to an alarm the same as asking them to respond to one, also doing it when you are actually going mobile isn't really advising them as quickly as you possibly could because generally at least four minutes would have passed from the time you received the call.