I have EIA and cough a good bit after a very hard ride, and the next day as well. Productively, as it's said. Yuckers. I'm training to be a DOM. But usually not during the ride. Cold weather makes it a good bit worse. I hardly notice it in the summer.

In your case, it might be allergies. Perhaps plants in your area release pollens at that time of day, this time of year.