I've noticed (in vanilla) that they mine and irrigate in a grid fashion on grassland, irrigate desert, mine or forest tundra, and mine all food bonus resources. I can't remember if plains are on the grid system or not, though I know they mine food bonuses there too. If I were to make an educated guess, they like to emphasize food production over production.
In vanilla they will change your improvements if, say, their culture expands into yours and your improvement doesn't fit into their grid, or if you've watered a food bonus, etc. Occasionally they will also run off multiple tiles and chain irrigation back to their cities if they don't have a domestic source. I've also noticed the "manic connecting" habit; I've used it to abduct and hold workers hostage while their homeland rots under pollution and goes un-improved. I can think of several times where I had 20+ workers herded and trapped on a single tile.