I looked at a few neuroscience papers which use that term and they don’t use it for a precise meaning. Only one of them mentions predictive firing (maybe, not sure it was talking about that) and all of them are mostly about prediction error. I agree papers should be precise about what they mean when they use the word prediction.
Off topic stuff
Yes but if they get strong enough excitation immediately, they can fire quicker than that. You see that in the most extreme case, where you directly inject current into the cell, no synapses involved. When it comes to synapses, some receptors produce EPSPs rising very quickly (much less than 20 ms), while others produce EPSPs which take longer to rise. Also, EPSPs can last longer than 20 ms, which just means the integration window is longer in effect sometimes. For metabotropic receptors it can be hundreds or thousands of milliseconds duration.
In the source I referenced, neurons in cortex fired within the 6 ms. From memory (I’ll find a source if you want), multiple layers fire around the sound time during the initial response. I think it’s everything besides L1, L2, L5a, and L6b, and of course some cells in the other (sub)layers.
L5b is about 10% of neurons (Number and Laminar Distribution of Neurons in a Thalamocortical Projection Column of Rat Vibrissal Cortex | Cerebral Cortex | Oxford Academic) and fires a lot more than other layers. I don’t know if it’s those 10%.
This isn’t known as far as I’m aware. We don’t know whether minicolumns extend through all layers, or are separate in each layer, or continue between some layers, maybe not adjacent layers. (for example L5a and L5b have separate minicolumns maybe: https://science.sciencemag.org/content/358/6363/610.full)