Might be a silly question but have you arranged for somewhere for the water to flow to when the butt is full?

If it's set up correctly, i.e. the overflow pipe connected to the drainpipe and the connection to the drainpipe is lower than the connection to the water butt, then everything should be ok, even in torrential rain.

Could you supply a photo of the connections?

It depends on the fill method/ type of diverter. Most diverters have to be level - the installation diagram will show you. If you bought the Sankey butt where the rainwater down pipe goes directly into the butt through the lid then you need to install an overflow pipe - the butt should have an indentation on the side (two/three inches down) to cut out for the pipe.