Zanshin is not about adrenaline or being hyped up. If anything, it is the opposite.
Zanshin is awareness, but not awareness of one thing. It is a general and complete awareness. Consider military tactics: If you want to catch your enemy off guard, you create a diversion. The person's attention and focus is placed on the diversion. While their focus is in one place, you attack from another. We apply similar tactics in kumite.
Zanshin is a state of awareness where you perceive what is going on around you, but do not mentally attach yourself to any one thing. We often perceive the difference in these two kinds of awareness when we fight people of different levels. If I am sparring a hesitant beginner, I can relax, watch his actions, and respond where appropriate. If I spar someone quite good, I fixate on particulars: his legendary reverse punch, the people watching, my ego. If I could relax my mind, let my ego go, and just respond, I would be at the top of my game.
We practice a type of mental awareness where we perceive what is in the room, as well as our own thoughts. We don't attach ourselves to any of them, but are aware of them. This is good practice for Zanshin.