As I explained, first, I don't believe that such people have the ability to detect a deity undetectable to those who become atheists.
Secondly, the claim is extraordinary, a one-off. To be believed, the empiricist needs evidence that points to a conscious, volitional agent that created the universe. Others don't. Their opinions about reality won't be the same as mine. They will admit any number of beliefs into their worldview that the empiricist would reject.
Third, I have the same experience that they are having, which I too once interpreted as a deity. I think I explained here the evidence that convinced me that I had been mistaken. I still get that feeling at times, but I understand it differently. It's a mental state characterized by a sense of awe and mystery, connection, and gratitude, and correlated with the release of oxytocin in the brain:
Effects of oxytocin administration on spirituality and emotional responses to meditation
Fourth, there's the fact that the reports of a deity don't resemble one another. There's a test to determine if others are seeing things invisible to you or either lying or mistaken - consensus or lack thereof. Maybe you're red-green colorblind, and one day it occurs to you that maybe you're being pranked. So, you prepare a collection of what you are told are red and green socks which are numbered so that you can tell which are allegedly green and which are red. Then you separate people and have them name the colors they see. You'll discover very quickly what is the case regarding these colors. Theists don't pass the sock test.
As you can see, I am trying to understand the reports of others in terms of what I know about reality including what I know about people, and to translate their words to mean something that conforms to that understanding. Another poster, a zealous Christian, and I were recently discussing what born again means when we discussing his and my definitions of Christian. He said that he defines Christian in terms of being born again, meaning a believer who is filled with the Spirit and is saved. I told him that for me, a Christian was anybody that believed the core doctrine of Christianity like he does, and that when someone say that they are born again, it doesn't mean to me what it does to him. I translate his words according to my worldview, in which claiming to be born again means having accepted the core doctrine of Christianity, but none of the rest, and that we essentially used the same definition once I removed the supernatural aspects of his definition.
Don't we all do that? Aren't you doing that now - trying to understand my words through the lens of your worldview? Some believers, maybe you, would be trying to understand me in terms of Satan and rebellion, some as I don't pray properly, or any other conclusion that assumes that a god exists that I just haven't found.
I don't think that most theists are frauds, just mistaken. As I said, I reject their conclusions because of the method they use to arrive at them. In my worldview, knowledge about reality comes from valid reasoning applied to the evidence of the senses to arrive at sound, demonstrably correct conclusions. Nothing else should be called knowledge, truth, or correct, including religious beliefs, which are believed by faith, not evidence. The believer will often point to the world or a holy book and say that that is his evidence for God, but it is not that when scrutinized critically.