Personally I disregard his presence and play around him. When I play adc and my boyfriend supports me he usually plays alistar and just headbutts him away from fights. Since most people float around Tahm, when he goes in for the headbutt he can easily knock up their adc and I can go to town unless they have an assassin. Tahm relies on his team for the most part unless he's one of those Grasp of Undying Tahm's and is in the jungle or top lane.
The only thing I can really suggest though is to be aware of how many stacks he has on you. I can't really stress that enough. I play support as well, and the best way to deal with Tahm is to keep him at a distance. If he uses his Q you can abuse him for a bit while it's down, because I doubt a Tahm player would straight up rush you to get his 3 stacks he needs to throw you into his team. If he did that, you could kite him easily.
Unfortunately though once he does eat you you're in for the ride. So if you make sure that you don't get 3 stacks on you, he won't. Your best bet though when it comes to Tahm is encourage your APC to damage him though. If I'm mid lane and playing against a Tahm I generally go Morello on the off chance that he has or will have a spirit visage, and unless they have another heavy healing champ on their team I throw my ignite on him and then go in to assassinate someone else. I'm a fan of Ahri and Fizz so generally this works for me. But it may not work for you.
Tahm doesn't enjoy being ignited. He's a lot like Mundo. Because of Tahm's grey health and shield, he would be forced into playing carefully. I can't recall the item but you can look into buying the one that applies healing reduction and builds into Last Whisperer if you're sure Tahm is the one carrying the game.