Whenever roads get upgraded they happen on the entirety of civ territory. Also when a city expands into a tile that has old road, the road is properly upgraded. However if you purchase (for gold) a tile that has an old road, the road stays as old road until the next mass-upgrade by era advancement.
Attached is the image, I am in modern era and I purchased the tile with cofee several turns ago and it has not upgraded, its still classical and costs 1 movement.
Attached is the image, I am in modern era and I purchased the tile with cofee several turns ago and it has not upgraded, its still classical and costs 1 movement.