Variations on Animal Companion's Support Triggers

[NielsenE]

I'm assuming this is intentional/RAW, but wanted to double check how others have read it:

Badger
Triggers on doing damage

Bear
Triggers on a strike hitting (but does not need to do damage)

Bird, Cat, Wolf
Triggers on a strike doing damage.

Dromaeosaur/Horse/Snake
Positional, movement based

So a badger's support action can be triggered by spells, while Bear, Bird, Cat,& Wolf are only triggered by melee/ranged strikes. (Spell attacks are not strikes under anything I've found). Is this correct?

[ofMars]

That seems correct

Do other party members benefit from Dromaeosaur's Support Ability?