Our backup last night caused most of the space to be consumed in our Flash Recovery Area. In looking at any obvious causes, I noticed that the TEMP tablespace had grown from about 100M to it's 5G limit. Is the TEMP tablespace included in an RMAN backup?
If the table space is temporary it should not be in the RMAN backup but if it is permanent it would be in the back up. So check to see which type it is if the data file shows in v$datafile it is permanent if it is in v$tempfile then it is temporary.