I so how got headstones without setting anyone to bury anyone or doing what needs to be done for the puzzle...I just came back to the game and they were there...is this a glitch? Will I get the trophy?

Do you remember if you got any sort of notification when you went back to the game? If your villagers passed while you were away, the game will give you a new "set" of villagers to continue the game, and the original ones will be buried without assistance from you or the new villagers.