Make sure the Instrument channel strip is record enabled, and then you should be able to record Ultrabeat MIDI data into Logic's Arrangement Window.
Are you using a MIDI controller in your setup?
If not, you can then use the CAPS Key. This will allow you then to use your Mac's keyboard to input the MIDI data.
If you look at the bottom left of Ultrabeat it says Pattern. Next to 'Pattern' is a block with dots in it.
Drag this block to the Ultrabeat channel on the Arrangement window, and this will add your Ultrabeat MIDI data to the arrangement.