Glad you got it sorted out.
The coreXY setup guide describes a motor test you can do to ensure things are moving correctly. Also, as you realized, just because it homes to the right place doesn't mean it's not mirrored, since you're able to correct for the mixup by specifying the direction of homing in your files.
https://duet3d.dozuki.com/Wiki/ConfiguringRepRapFirmwareCoreXYPrinter#Section_Movement_section
For a CoreXY or H-Bot machine, RepRapFirmware assumes that the motor connected to the X motor output moves the head in the +X and +Y directions when it runs forwards, and that the Y motor moves the head in +X and -Y directions when it runs forwards. [Note: firmware 1.18 and earlier assumes that the motor connected to the Y motor output moves the head in the -X and +Y directions when it runs forwards]. So you can start with these M569 commands in config.g:
M569 P0 S0 ; X motor runs forwards
M569 P1 S0 ; Y motor runs forwards
Then test for the correct X motor movement by sending these commands from the console:
G91
G1 S2 X10 F3000
If the head moves diagonally in the +X and +Y directions, all is well. If it moves in the -X and -Y directions, change the S parameter to S1 in the M569 P0 command. If it moves towards +X and -Y, or towards -X and +Y, turn the power off and swap the X and Y motor connections.
When you have the X motor moving correctly, test the Y motor by sending from the console:
G91
G1 S2 Y10 F3000
For firmware 1.19 and later: If the head moves diagonally in the +X and -Y directions, all is well. If it moves in the -X and +Y directions, change the S parameter in the M569 P1 command to S1.
For firmware 1.18 and earlier: If the head moves diagonally in the -X and +Y directions, all is well. If it moves in the +X and -Y directions, change the S parameter in the M569 P1 command to S1.
Important: make sure that you have chosen a right-hand axis system. That is, looking down on the printer the +Y direction should be 90 degrees anticlockwise from the +X direction. If instead it is 90 degrees clockwise, you have a left-hand axis system, which will give you mirror-image prints.
