Speaking from experience of broadcasting when a fire alarm goes off, making sure you get out of the building safely is more important than making sure that going into back up material is done smoothly.
Indeed, and it depends on how much notice the studio gets. I just listened to the bit where it happened and they were interviewing someone down the line and just faded her out an into an emergency tape, which oddly was already half way through a song. Presumably no time to interrupt and say anything. I hope they had enough time to tell her what was going on before they got out!
I'd assume they have a two-stage system, like they do in London and Manchester. If they have an amber light illuminate, then they can continue with the programme whilst the situation is being investigated, but they should be prepared to evacuate at any time. If the red light illuminates, then they need to evacuate immediately.
What normally happens is that when a device (such as a smoke detector or a call point) in the fire alarm system is activated, the affected area goes straight into red, and other sections of the building go to amber. The rest of the building will only go to red if a second device is activated, a safety marshal confirms the need to evacuate, or nobody is able to confirm reset the system within a set time period. If there is no danger discovered, the system is reset, and operations continue as usual.
I'd assume the lack of any message explaining the situation will have occurred because either the studios were in an area close to the activation which went to red immediately, or the fire was confirmed almost immediately by the activation of a second device and the whole building went to red within seconds of being put into amber.
As is demonstrated on this clip from Chris Moyles on Radio 1.