[Longman](https://www.ldoceonline.com/dictionary/come-down) 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 of the falling:

- The cans came crashing down.
- Jack and Jill came tumbling 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.