I just figured it out, I can't believe I didn't just realise that before. So obvious.
There's this setting in Cinnamon/Workspaces "Only use workspaces on primary monitor"
The windows that are shown on all workspaces are systematically the ones in my laptop screen, the ones in the external monitor have their independant workspaces.
Custom build w/ Gigabyte Z87MX-D3h | Intel Core i5 4670 | 8GB DD3 | 250GB SSD