Just another thought.
The DMX Operator has a DMX polarity switch, which ideally you should never need to change. Perhaps it got flipped my mistake? It can't hurt to try. If this unit is in a rack and not accessible, this probably isn't a problem.
It could also be a loose cable, but that can be difficult to nail down with the cables inline. For testing loose cables or pins, it's best to get a cable tester involved. There are a wide range of cable testers including devices sold as cable testers to using a multi-meter and justin using the ohms test with tone to test it out.
I typically power my console up first, then the fixtures, but when that doesn't happen, it's typically the stage being wired up and powered up and then with the console or MyDMX dongle ready to go, DMX is connected there. Never had any problems related to order of power up.
Jingles is big on recommending the Opt-Branch4 right now. I'm going to be buying one soon myself. Just sounds like flat out good practice to me. I doubt you are using them.
Try the switch. If need be, even if with microphone cable, test each cable and ensure a 1:1 relationship on all 3 pins on each cable. But, I'd recommend the investment in DMX cable, which won't be that expensive. Also, take apart that DMX terminator and ensure it is in fact a DMX terminator and not someone who just crammed a plug into an outlet.
Also, test fixtures one at a time direct to the DMX Operator. You might as well ensure that if this is your new job, you know it inside and out. That's why I only use my own gear, I can always feel comfortable knowing tht whatever the problem is, I am in control(or at least given the impression that I am in control).
Another thing to look at is the Fade Time slider. Maybe move it down, which I think will speed up how long it takes to change scene or your changes. This might be it as well.