Restore app windows to their original Spaces When re-opening an app, all of its windows end up on the first Space, regardless of their original placement:

Original layout: one app has two windows open, each in a separate Space

+-----[ Space 1 ]-----+  +-----[ Space 2 ]-----+
|                     |  |                     |
|  [Chrome window 1]  |  |  [Chrome window 2]  |
|                     |  |                     |
|                     |  |                     |
+---------------------+  +---------------------+


Incorrect layout after app restart: both windows are in the first Space

+-----[ Space 1 ]-----+  +-----[ Space 2 ]-----+
|                     |  |                     |
|  [Chrome window 1]  |  |                     |
|  [Chrome window 2]  |  |                     |
|                     |  |                     |
+---------------------+  +---------------------+




Is there a setting or an app that would make it possible to have apps restore their windows in the Spaces they were originally located before the app was quit?
edit 2:  This still doesn't COMPLETELY work for me as well: some windows are restored and some are not. The new bug id in Chromium is 1012034, and it still needs your votes!

edit: It was implemented in the latest development version (Chrome 79)!

Though, by default, in compliance with Apple's UI requirements, this feature still won't restore the workspaces if you exited Chrome with Cmd-Q. Quoting sdy, the feature author:


  For folks who want Chrome to always restore windows to their original spaces, you can set that by running this command in a terminal window (for Canary, use com.google.Chrome.canary):

defaults write com.google.Chrome NSWindowRestoresWorkspaceAtLaunch -bool YES

  
  To go back to the default behavior, run:

defaults delete com.google.Chrome NSWindowRestoresWorkspaceAtLaunch



Original answer:
There is a bug #74812 in Chromium. Vote for it!

Same question on Superuser.