There is Godus which I always thought of as a precursor to islanders. It has more elements to interrupt the player but it has the sake overall aesthetic and feel.
Edit:
I played this ages ago and the reviews after some updates are very negative so it sounds like it’s no longer the game I played.
Slow Down With These Serene City-Building Games (www.wired.com)
I am looking for more games like this: though this list seems like a good starting point....
Gamers. What was the game that got you into the hobby?