Where do save files for Xbox 360 games save to on Xbox One?

I just recently got an Xbox One X after upgrading from an original Xbox One. All of my save data for my Xbox One games transferred over onto my new console without having to transfer them to an external hard drive. However, 2 of my backwards compatible 360 games that I was playing (Beyond Good and Evil HD and Deus Ex: Human Revolution) which I had stored on the internal drive of my old Xbox One did not transfer over. I installed both games onto my new Xbox One X and all my old save files have not transferred over. I did not get the option to save my 360 games to the cloud so I assumed by default they did that anyway like the One games all do.

Would the game files have only saved onto the internal hard-drive and would I have had to transfer them over manually? For some reason when playing 360 games I am not connected to Xbox live according to the 360 hub but when I press my controller's Home button and go back to the Xbox One's home page I am still connected. If I did not transfer the files manually does that mean I have lost them?

Check your cloud, mine always did so automatically.

if it is stored in the cloud then you should be good if not you will lose them.

@Random_Matt: how can I check my cloud for saves?

Have you installed and started a new game? Upon starting a game, saves should then download automatically. Manually checking: https://support.xbox.com/en-GB/games/game-setup/cloud-game-saves-faq

@Random_Matt: I started up both games but when I selected "load game" both games said there was no saved game data.