Tiberius has no damage fall off, meaning 650 damage every .7 seconds and .49 seconds no matter what range you're at. The best counter is someone like eminence Lian or a sniper who can deal more damage than Tiberius from afar.
Tiberius can be damage immune during the whirling blade part of his ult. Use someone like Io or Ash, people who can cc him off the map. He can't use another move until he lands in his whirling blade stance, so he'll fall to his death.
Pick up resilience for heavy blade, or it'll slow you for 3 seconds. You could also pick up someone like Atlas who can catch the heavy blade, someone like Zhin/Koga who can cleanse the slow, or someone like totemic ward Grohk to prevent the slow.
Tiberius deals 650 damage every .7 seconds, and .49 seconds during combat trance. That's a burst of 1300 every second for 4 seconds. Your best bet is to use someone like Lian to outburst him, or someone who can avoid his burst.