Question:> I want you to paint my kitchen cabinets. Should I wait to have the counter tops installed or does this matter?
Answer: It doesn't usually matter what order, however, I'd do them before you install new countertops as this is usually how it goes with new cabinet installs. Meaning, cabinets are always installed first, followed by the counter tops. Painting them first is standard procedure.
We can paint cabinets before or after. Its highly unlikely counter tops would ever impose a problem to the installer or suffer damage from the installation of new counter-tops. They measure to fit and its a no compromise there. They also just sit on top of your cabinet frame and don't touch anywhere that imposes an issue. If by chance something something happen to the frame, touching up is as easy as a call away.
Being said, if the cabinets should sustain unexpected minor nicks from anything for that matter, assuming we aren't talking about refinishing a door from a massive impact... I would most likely do minor touch-ups as a free service.
The back-splash has more relationship to the painting which falls under painting rooms, walls etc.