[Card] Hate

Hmm, I don't think the stack/chain quite works that way.

Your opponent pays the needed resources, and then reveals the card. Paying a cost is regarded as a part of playing the card. Thus there is no chance of playing actions between paying and playing the card.
After your opponent's unit has been paid, it is revealed from his hand and he decides where the unit goes. Playing a unit/support is regarded an action, so you DO have a chance to react to this unit hitting the desk. But do notice, your response can't do anything about the resources used to pay for this unit, as paying was a part of playing it (also note that units/supports don't stack/chain). Thus playing Hate in that situation doesn't affect the unit. And it's the same thing even if your opponent played a tactic.

If you want to restrain your opponent from playing costly units, you need to play Hate after your opponent's Kingdom phase or Quest phase.