I think on me, coffee (and paracetamol) act psychosomatic before they ever have a chance to.

Another explanation is that it's like reserves. If her plane is gliding just above the treetops, and you say "can you do a barrel roll", she'll just not, but if you fill her tank up first, she can safely, even if it doesn't actually use any more fuel than she had before. That is, you don't want to get embroiled, but once you *have* tea, then you're safe, so you can start to wake up without fear of having to think without caffeine :)