I don't think this can be the problem. But you will have to be more specific about what exactly you do, and what exactly then doesn't work. When I use Edge with the example Diagram for Capablanca in the Interactive Diagrams article, play f4, f5, open the AI bar, copy the game displayed at the bottom of it, reload the page so that I get a fresh Diagram, and then paste the game back, it advances both f-Pawns. I can then play Nh3, and it replies with e5. That is all exactly as it should be.
I don't think this can be the problem. But you will have to be more specific about what exactly you do, and what exactly then doesn't work. When I use Edge with the example Diagram for Capablanca in the Interactive Diagrams article, play f4, f5, open the AI bar, copy the game displayed at the bottom of it, reload the page so that I get a fresh Diagram, and then paste the game back, it advances both f-Pawns. I can then play Nh3, and it replies with e5. That is all exactly as it should be.