The program modes are run from the fixture itself. This means that the My DMX 3.0 software does not control the show to keep the lights in sync. Most fixtures that have built-in program modes allow the fixtures to talk to each other via DMX in a master / slave configuration. I have not found a way to make this work via DMX software only hard settings on the fixtures so it's all or nothing with that.
On a longer note - you could program chase scenes with pre-programmed colors and movements. This of course could take a lot of time and would always run exactly the same exact way.
I would recommend checking the manual from your fixtures to see about master / slave mode and the understanding that is not controls via DMX. The DMX software only tells each fixture to run a program from itself. This means the programs run independent from each other.
I am sure you will continue to find limitations and nuances to drive you crazy - good luck in your DMX adventures!