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.
One famous example of this usage, which has doubtless popularised it, is from the old spiritual/hymn:
Joshua fought[/fit] the battle of Jericho ... Jericho ... Jericho;
Joshua fought the battle of Jericho
And the walls came tumbling down.