This has for long been an issue when casting from and android device (have not tested IOS) to chromecast.
Almost every time the playlist will start playing from the beginning when the song which is playing when you connect to a chromecast is over instead of the next song in the playlist. I am not alone in experiencing this.
The problem seems to be more prevalent when you have multiple devices online at the same time, I usually have my windows 10 client running when connecting from my phone (oneplus2 android 6.0.1) and the only way to not have the playlist starting over is toggling shuffle on.
Hey @mr_curry!
We'll be closing this thread since we haven't heard back from you in a while.
If you need our help, don't hesitate to open up a new thread.
All the best.