Longman gives the appropriate sense of what it labels the phrasal verb usage here:
come down phrasal verb
...
3 to fall to the ground
- A lot of trees came down in the storm.
- We were still out in the fields when the rain started coming down.
I'd say that there is enough cohesion between 'come' and 'down' here to justify its being considered a multi-word verb:
- The trees came down in the storm.
- The trees fell [to the ground] in the storm.
In spite of the cohesion, it is possible to insert ing-forms between 'come' and 'down' to describe the manner and/or degree of the falling:
- The cans came crashing down.
- Jack and Jill came tumbling down.
- The rain came bucketing down.
- The ash keys came spiralling down.
Whether or not one considers come V-ing down as cohesive enough to also be considered multi-word verbs (of a different class) is open to debate. Certainly
- The ash keys spiralled to the ground (etc)
is available for
- The ash keys came spiralling down [to the ground].
The grammar is fairly idiosyncratic ('went V-ing up' is unusual), but these expressions are idiomatic (commonly used and accepted), so they arguably qualify as idioms.