Well, I guess I will disagree here. To me next means, well, next. So next sunday (being that today is sat) is tomorrow. If you say next Wed, that's the 25th or whatever.
If you are meaning say Sun 28th, then to me it should be a week from now/tomorrow type of thing.
But anyways to me that is what makes sense. But I don't think I am in the majority here, so I would likely discard what I think

.
Edit to add: its the same thing when you are driving. When you say "take the next right"....to me that is literally the right coming up (i.e. the literal next one). You don't say "take the next right" and expect the person to wait until the 2nd right.
Again, thoguh, that's just me....