As suggested, I only read the conclusion of Dissociative Experience and Cultural Neuroscience: Narrative, Metaphor and Mechanism. So I think the paper's more about how to study the phenomenon than how to explain it? Anyway...
Here's my usual non-scientific speculation. (I only recall reading somewhere that--as in some religious experiences--there's a part of the brain that becomes inactive during glossolalia. This part of the brain usually holds focus for attention in consciousness. I don't mind being corrected here!)
Firstly, it wouldn't sound far fetched to me if the neurology of such babbling is much like the neurology of babies babbling naturally, as if by instinct. Perhaps the ability to babble comes first, followed in life by learning how to focus the babble into coherent speech. If this is a reasonable assumption, then one question about it is "what eventually causes strong inhibition of the incoherent babbling". I wouldn't even be surprised if studying other baby-to-adult animal vocalization behaviors help here.
Secondly, especially in the case of humans, the functionality of (and "reason for") language is to communicate socially, for numerous pro-survival benefits. As (I think?) I've mentioned elsewhere, I speculate that human social behavior and human tendency to feel spiritually connected might be related, neurologically. I don't mean that such connections naturally lead to thoughts of God--or at least not until humans eventually added words like "God" to their vocabulary, but I do mean that such perceptions of spiritual connectivity probably coincided with beneficial (selection-wise) feelings of connectedness with other beings, and the rest of the world. I.e. we only learn to manipulate the world (and beings) around us by first feeling connections with it/others.
To get to the point of the "Secondly" paragraph (above, without blabbing speculatively on and on) is that the human behavior of speaking in tongues to me seems like further evidence that may help support theories to explain evo-psych origins of lingual-social-spiritual behavior.
Before anyone spanks me for being so speculative-sans-science; ok, I'd be happy even if these ideas were only stated in science fiction, somewhere! (Admittedly, I don't read enough, in any case.)
But I can't stop there. I have to add that Thirdly, these lingual-social-spiritual behaviors also seem to be linked in the should vs shouldn't (i.e. prescriptive/proscriptive) parts of our neurological processes. I.e., the socially pervasive prescriptions/proscriptions of language rules, social graces vs faux pas, and perhaps peer pressure to believe (dare I say snobbishly) in the same in spiritual preconcptions, gods, etc.
(Am I making any sense here? The focus is SIT, so don't let us diverge far from that. Shoot, and I want to talk about human empathy in all this, too. Oh well.)