Always a tricky thing, this dealing with a boxer or kickboxer, for instance, who has a fast jab. Tricky because of the speed, the followup with the other hand, and the fact that often they are used to getting hit and won't necessarily respond to atemi - sometimes yes sometimes no in my experience.
Some things that may help to understand - deal with the whole person but don't forget the actual attack - meaning evade and enter so you have better position and can take what's offered from there, not at the range of the punch, and also deal with their mind/intention. Another thing, it's pretty well-established that you won't catch the jabbing hand, so don't try, you'll just get hit with the cross. Try practicing following the jab in and checking the elbow or just the bicep (really just below the shoulder) - that especially doesn't move through the range of the hand but stays relatively in one space that you can track easily. That is one way of actually getting a kote-gaeshi, but it's donwe tight, not with a big circle or lead. The trick is entering and not getting hit with the follow-up punch.
Last, something that may help also is the notion of dealing with the person, not the attack - this is why someone would use atemi, but there are sometimes better (in the case of someone who will not react) ways of leading the mind and interupting them for your entry - this is hard to explain - a flurry of hand movement while moving in to "beat down" any punches, things like this can be effective but you must enter fast and with total commitment - that's why it takes a lot of practice.