I get this if i apply lather then press a hot towel into it for a minute or so.I get it when i get a hot towel shave from the barber.I reckon its just the soap or cream doing its job.I quite like it lol
I guess that would depend on the soap ingredients. I could see where menthol or eucalyptus might tickle a little after being applied and sit for a while.
I doubt this is the reason but if the soapmaker doesn't neutralize the lye entirely it can cause a mild tingling sensation (and go all the way to burning you depending on the final pH). Like I said, it's doubtful if the maker is well established that this would be the cause... most even do a pH test on each batch to make sure the oils and fats are fully saponified.