From playing the Witch Doctor, with my friend as a Wizard, I have seen all variances in relation to attack speed, especially during periods of increased attack speed through shrines and other interactions.
Channeled Spells like the Witch Doctor's Firebats appears to impart damage more frequently with increased attack damage. Especially useful, as resource usage is based off time, and thus you are gaining more damage without expending more resource.
Summons like the Witch Doctor's Gargantuan may summon slightly faster, but pets and minions have a set attack speed, and are not influenced by your current or increased attack speed. While Fire and Forget spells bring out a pet that stays in place, and expires, the same rules apply.
Damage Over Time effects like the Witch Doctor's Haunt tick over more quickly with increased attack speed, so although they will deal the same amount of damage, it will take less time for them to do so.