This is actually why I don’t do it. All it takes is that he teleports away from you, you whiff, and then he teleports again and hits you on your recovery. He still has the advantage. Even more worrisome is that, at least as far as I can tell, you can’t even tell where he’s going to teleport to, until he’s already there.
Pretty much what Sasuke said. Proper counter to Fulgore teleport is to toss out a normal as (more or less) he’s disappearing from the other side of the screen. If you have a spammable light that chains, that’ll probably be the button of choice. You can’t react to him appearing beside you - you have to preempt him becoming visible near you to get the punish.
It’s stupidly annoying because you have to just throw out normals and hope that the Fulgore decided to go in at that point, but it will work with some practice. Look at Finchomatic’s 2nd video (post #14) to get an idea of the timing.
Unless you’re whiffing a normal with a fairly large amount of recovery (Aganos with chunks perhaps?), there’s no chance Fulgore gets to teleport again near you before you can recover and toss out another one. I use Hisako’s cr.MK to catch teleports (since her lights don’t chain on hit), and I have to royally muck up the timing to get caught on my recovery.
Of course, you had to say that, because you know it to be true… 
Also, I can’t look at the video because I’m still suffering from Internet connection issues. 
Ah. I feel like even with chunks (say 2) Aganos should have some button that will serve to catch teleports. I’m a little fuzzy on his frame data with chunks though. I think LK is his fastest button, no? As long as it hits and recovers at least as fast a Hisako cr.MK, it should serve to check Fulgore on any teleport in neutral.
@Infilament @MBABanemobius - any idea on the frame data for Aganos’ fastest normal with 2 chunks?
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No. Even that move has enough time. His teleport is slower than it seems.
Aganos standing LK:
0c: 5f
1c: 5f
2c: 5f
3c: 6f
4c: 7f
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I went into the lab and tried countering it (as Aganos). The results are “iffy” at best. With no chunks, I actually found it hard to poke Fulgore with s.LK, not because it wasn’t fast enough, but because the attack would complete BEFORE he reappeared and would whiff (thus getting me hit by the throw and the DP, regardless of which Fulgore did). I had more luck, believe it or not with c.HK of all things, because I could start it earlier and count on it knocking Fulgore down as he appeared. The unfortunate thing, however, is that this does not apply when Fulgore appears behind me. When he does that, he hits me no matter what, because the time it takes for Aganos (and I assume any character) to turn around, he’s already hitting you. Thankfully, I’ve already developed a strategy to put walls behind me whenever I’m fighting against Fulgore - that way, if he tries to do a teleport crossup, it puts him into a corner. All in all, still “iffy” though.
I will grant you that his teleport is slower than I expected. 
Thanks Infil 
So yes, @GalacticGeek - even with full chunks, Aganos has normals fast enough to challenge Fulgore’s teleport. I can’t imagine they recover slow enough (even in high chunk scenarios) that he can’t get another LK out before Fulgore gets to teleport again.
EDIT: Yeah…I wouldn’t recommend doing super slow, high recovery buttons to challenge with. I strongly suggest simply practicing with your faster button to get the timing down - it is a GUARANTEED punish on a teleporting Fulgore if you get it down pat.
NOT if he teleports behind me, which most Fulgore players are likely to do.
If you get the timing down you will hit the move in way that catches him whether he teleports in from or on the back.
What he said^^
Not necessarily. In order for that to happen (assuming you’re correct), I would have to adjust to the timing of a frontal teleport and rear teleport separately, because with the latter, I have to account for the fact that my character is going to waste frames of animation to turn around, which leaves him more vulnerable. So, it’s not just practicing the timing for 1 scenario; it’s practicing for 2. Furthermore, it seems to me that everyone is assuming that he’s going to appear right next to me - he might not. If the Fulgore knows his spacing, he’ll teleport a slight distance away to cause me to whiff and hit me with his extended-range invincible-on-startup DP anyways (sans chunks, of course).
What they’re saying is that, if you find the right timing, your character will either hit Fulgore in the front, have already turned around so you can hit Fulgore in the back, and if he teleports away then your attack is fast enough to recover before Fulgore can hit you.
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I’ll keep practicing it, don’t get me wrong, but right now, I don’t think there is “an already turned around so you can hit Fulgore in the back” scenario when it comes to using pokes - especially with Aganos. The only time that I can collectively recall successfully hitting him in the back post-teleport is when I hold shadow natural disaster and the cyborg teleports himself into it, and that requires both luck, and meter.
Aganos doesn’t come into play here, because he has a 5 frame normal and he doesn’t turn around slower than other characters.
The timing exists, you just have to find it.
I thought all other characters had 4-frame normals. Or is that just with throws?
I call them 5 frame normals, sorry. Aganos has what KI calls a 4 frame normal just like everyone.
So everyone has 4-frame normals, then? Throws are still 4-frames, right? Why do you call them 5 if they’re actually 4?
Everyone has a normal that has 4 frames of non-hitting startup, then hits on the 5th frame. KI calls these 4f normals, I call them 5f because I like to measure the time it takes for the attack to actually hit you.
Throws hit on the 5th frame (ie, they are as fast as the fastest normal).