I have noticed lower chapter level islands that have several animated items. I have only seen animation..

Most of the animated decorations were available for special purchase for real money in the past. A couple others were grand prizes from seasonal sets.Two of them, Center Stage (spinning dancing girl) and One Man Band, were prizes for the game's first and second anniversaries. Hopefully, the next anniversary in October, will offer another.

So there's no trick. But keep playing for a long time, play slowly so you won't get caught up with developers, and the game will still provide lots of fun and surprises.