No, he didn't. That's what Paul Joyce tweeted, but it isn't what Koeman actually said. This is what I mean about the headlines. What he actually said, word for word was: "He started at the weekend, that is no reason to have doubts about his future with Everton".he actually said 'James McCarthy's future lies with Everton'
Note the use of 'that'. Not "there is no reason to have doubts about his future with Everton", not "hopefully his future will be with Everton" and certainly not "James McCarthy's future lies with Everton", just a comment that playing in our most recent game is not a very good reason for assuming somebody is on their way out.
I'm not saying he will be leaving, just that the quotes were nowhere near as emphatic as you're making out.