Mach will only move where it is told to go. Normally your code will define the toolchange position on a lathe, this is because it is tool dependent as to where the best position would be and on a lathe with a turret the axes do not have to be in any specific position for you to do the toolchange, unlike a lot of milling machines.
If you prefer to have a set toolchange position then you can write that into your M6start macro or you could even have the macro look at a couple of User DROs which you use to enter a toolchange position.
The only problem you may have with these methods is that, as mentioned, on a lathe it is tool dependent as to where the safest position would be, also getting to that position may well be tool dependent.
For example on a mill it is almost always safe to raise the Z fully then move X and Y, on a lathe it may be X has to move first then Z or maybe Z first then X or maybe it will be possible to move both at the same time, it will depend on the current tool and also the next one that will be presented.
Hood