If "delete" command is used then node is not removed from public instance. It's only removed from author. Correct behaviour should be that the node is removed from both instances.

"markAsDeleted" command works as expected. When node is marked as deleted then you have to confirm deletion by "Publish deletion" and then node is correctly deactivated from public instance.

How to reproduce:
1. The easiest way is use configuration app where "delete" command is used.
2. For example under /modules/core create node named "TestDeletion"
3. Activate "TestDeletion" node and check if node exist on public instance
4. Remove "TestDeletion" node from author instance
5. "TestDeletion" node still exist on public instance