Haste only affects one targeted minion.
It only lasts 1 second according to the description.
And the Ignite effect helps kill the minion faster.
The problem here seems to me to be with this haste buff that only lasts for one second. Hate is just a movement speed bonus of +30 %.
Suggestion : I think Haste should be permanently given to the targeted minion (as far as the minion as a Dread Shame upon here it I mean).