Having 'this Tuesday' and 'next Tuesday' mean the same thing is the exactly the sort of thinking I've came to expect from our Hair. I bet he's got a million anecdotes involving turning up to meetings, appointments and dogging sessions a week early.
Next Tuesday means this Tuesday. (But you should probably use this tuesday, it's clearer). Tuesday next means the one after. Now shut it, scrubs.
Quite how a bunch of English natives, especially little Englander brexiter types like hair, need a foreigner to explain this to them, I have no idea. Shame on yous, you should be deported, the lot of you, and some people from my village could take your place.