I just returned from a seminar with Tissier-sensei in Montreal. His speed comes from relaxation; he emphasizes the principles of maintaining natural postures, finding the best position relative to the attack, and then applying the technique without muscular force. I've practiced Aikido for over 25 years, and this was an intense learning experience.
His movements are based on Kashima Shinto-ryu Kenjutsu footwork while Tamura Sensei's style relies heavily on Iaido. That's why Tissier Sensei's Aikido has so broad movement in techniques and Tamura Sensei has much more narrow technique and economy of footwork. Brilliant and astonishing display.
Actually, it's the Kashima Shin Ryu School of Kenjutsu, the one that Seigo Yamaguchi and Christian Tissier have followed. Kashima Shinto Ruy is a different school. After some research, you can find they are different schools within the same region in Japan. :)