Have you tried it yet? It won't let me play it on my US account...
It says I need to purchase a license to play.
Edit: Got it working, just need to make sure that your JP account has the PS4 you're using set as your primary system.
There are digital download versions for both PS3 and PS4. I believe it's not Cross-buy though, so yeah, you will need to buy both versions eventually if you want to play on PS3 and PS4.