My cats and Tortoise seem to get along fine. If the cat is laying down and the Tortoise is walking in that direction she will pretty much walk over the cat unless the cat moves. The only thing close to aggression was the one time my big cat went over and bopped the Tortoise on top of the shell once with his paw. No problems after that.
My house seems to be the depository for stray cats, and right now I have 8 of them that I have had spayed and neutered. I feed them and treat them as my own. Naturally I have favorites and some not so favorite. None of these cats has ever given the tortoises a second look. These are cats that came to me full grown, not as kittens that were raised with turtles.
Every so often I will find a baby box turtle out in the open someplace, not in a box turtle yard, and my guess is that either a bird dropped it or a cat was playing with it.
I don't think you have anything to worry about with cats and larger-than-hatchling turtles/tortoises.
My cats completely ok with franklin inside, but when the cat was still going outside you'd have to watch them together because sometimes he was nothing and sometimes he was prey. Thankfully the cat only ever booped the shell because that's what was mostly visible over grass to him. Inside the cat could care less that he even exists. But it I put Franklin with my cat when he's curled up in bed the cat is NOT happy and gets up and leaves, franklin just loves to burrow into his soft warm fuzzy belly lol. My avatar picture is actually a picture of their first meeting.
I'm having a problem with keeping the strays out of my enclosure. I'm worried they are pooping in there and they are always trying to drink the turtle water. I'm at my wits end with these cats here. They poop right in the grass and my kids play there...grrrr. The cats never bother the turtle but I do think they have taken her fruit and veggies before.