Gang Busters was a famous radio program that was first heard in 1936 and aired until 1957. The sound effects of police sirens, tommyguns, and screeching tires that opened the show were dramatic and exciting -- this inspired the expression 'coming on like gangbusters'.
Usage has opened up to describe things that are not just exciting, but successful, intense, and many other adjectives, and many drop the 'coming on like' prefix. I think we should be more careful about how we use it, and keep it true to its origin -- something that starts with much excitement and drama is 'coming on like gangbusters'.
The rainstorm late last night came on like gangbusters!