Ok there are two coordinate systems in Mach, in fact in any CNC. You have Machine Coordinates and Work Offset Coordinates.
Machine coords are mainly for Mach so that it can keep track of where it is, the user mainly needs the work offsets.
The Machine coords are set by homing. When you home the machine it will move to the switches and back off and then set the machine coords zero where your home switches are. Now normal convention dictates that machine zero is X fully negative, Y fully negative and Z fully positive, thus all X and Y moves in machine coords are positive and Z negative.
This only works if your machine homes fully negative X and Y and positive Z.
It sounds to me like you are homing so that when at home position the tool is fully positive on X and Y. This is not really an issue but can be problematic if you wish to reference machine coords and dont really have a good idea what or where they are, it is much easier to envisage machine zero as being lower left (think of a graph on paper, X and Y zero is lower left).
So to get around that what you do is set a home off value equal to the distance the axis in question is away from being fully negative. Doing that will mean when you home your machine the machine coords will not read zero but instead will read the distance (in a positive value for X and Y and negative for z) that your machine is away from machine zero. Thus if you commanded a G53 G0 X0 YO the machine would move fully negative.
Doing that will allow you to set Soft limits for X and Y min and Z Max as zero and set X and Y Max and Z Min as the distance of each axis (Z will of course be a negative number)
Now Work offset coords, they are the ones the user usually watches and deals with, they can start anywhere you like on your table, for example you may wish to have work offset zero as the middle of your travels, so you would jog to the position you wish zero to be then press the zero at the side of each DRO and you have now just set up a work offset. If you regenerate the toolpath you will see your work is now where you want it.
Now the Table view in Mach, it has changed a bit from the time the videos were done, the white dotted line is the way it is now also when you change between table and work views you need to press Regen after to see the proper view.
So to summarise, you can keep the machine coords the way you have them now if you wish or you could change them as detailed (Home Off value) to follow convention, its up to you on that one

Hood