Solid Wood Stairs are not the problem. I do tons of work on 100 year old homes and they all have solid treads. Judging by the picture, yours are only 3/4" thick, they really should be 1" but that isn't the real problem anyway.
Moisture was the culprit, as has already been mentioned dehumidifier=good. I also recommend painting the bottoms of the treads. What happens is the bottom side is getting wet and it expands, the top, being relatively protected from moisture by the urethane stays relatively dry and does not expand causing the wood to warp.
Liquid nails is bad juju for stairs, or any flooring application for that matter. It fails when you don't want it to and won't fail when you need to take it apart (someone like me will curse you in 20-40 years when something needs to be fixed). Properly installed you can always get everything to stay together without liquid nails.
This link goes over the best practices of hardwood floor care.
How to take care of your wood floors - Saint Louis Wood Floors