When duplicating a tilemap by copying components with code

A project which reproduces this is attached

Steps to reproduce:
1) Open attached project
2) Open scene Test1
3) Expand 'Grid' in the Hierarchy - observe children Tilemap and TilemapDupe
4) Tilemap has components Tilemap and TilemapRenderer. TilemapDupe has the script DuplicateTilemap attached
5) Click play
6) Observe that the Game Object TilemapDupe now has components Tilemap and Tilemap Renderer, but the tiles are not rendering in the scene
7) Click on Tilemap and copy component 'Tilemap'
8) 'Paste Component Values' on the Tilemap component of TilemapDupe
9) Observe that the tilemap now renders, even though no actual values changed in the component

Also present in 2018.2 and 2018.1