difference between machine coordinate systems and CAD software

I have a problem with the system coordinates, I have represented the machine axes in blue (when I click on the + button in axis and on each axis).
and the axes I need to orientate on fusion 360 so that the cnc machines in the right place (in red).

would the problem come from fusion or axis?

I have another cnc with another control card (edingcnc) and I don't have this problem.
 

 

I think your X axis needs to be rotated in F360 so its the same direction of the machine movement.

Your fist picture = you are looking at the part from behind, any particular reason for it?
Moving table and moving head are two different types of machines, despite being the same functionally, but very different when looking at them and using them, i have a feeling you are mixing these.

Machine coordinates are always defined with respect to tool movement on the workpiece regardless if it's the spindle or the workpiece that moves. So presuming that the blue coordinate system represents the tool movement on the workpiece then that is a common setup for a mill. Having the X axis pointing to the left in the CAD system is not wrong (you just have to rotate the part on the machine table) but a bit unusual.

With the other control does the axis jog the same direction? X+ = X+ travel on both machines.
If the jog is correct is the Post the same?

it's actually my mistake, I didn't remember that the Machine coordinate was related to the spindle displacement (I'm used to it with cnc gantry).
What would be the quickest and easiest way to correct my mistake?

With no hardware info, this is just a guess. If you have encoder feedback, swap A and B to reverse count.
For steppers, invert direction.

Be ready with E-STOP when you test, things can go very wrong quickly.