Its interesting that the answer to the OP depends on what side your on. Alarmist implies an exaggerated claim. Climate deniers are not using the term to possibly concede the severity of the situation, they are using it to call the claimant a liar. So, Ad hom.
But in some cases the climate deniers may have a point there. Some claims about climate change have no doubt been quite alarmist. "The world is going to end in 12 years," and so forth.
Just the same, some of us may consider that a justifiable exaggeration to scare people into immediate action.
At any rate, whether or not a given claim is "alarmist" is a matter of opinion, not really a logical fallacy
per se. And even if a particular claim is exaggerated, that doesn't invalidate the entirety of climate science.
But as someone who has studied climate change and understands the science, my internal monologue responds, "You're damned right I'm alarmist - we should all be alarmed." So, non-seq as well?
I would start by establishing which specific claims the denier considered alarmist, and then examining the substance of the claim, comparing it to known facts about current trends, and going from there.
It may be that they're just ill-informed about the severity of the situation, or they may have a point. If the claim they're citing is indeed alarmist, then the most intellectually honest route is to acknowledge that everybody on our side is not correct 100% of the time, but that doesn't mean climate change is not a dire threat. Then make an effort to avoid hyperbole and keep the conversation rooted in facts going forward.