I think the Home World Gems wanted to harvest resources from Earth. The machines look like drill mines designed to find and collect minerals from the earth's crust. The clones may either be labourers or just to expand their army. Have you noticed that Amethyst's weapon looks like a slave whip? That probably doesn't mean anything, but it could be.
From the amount of machines, the Gem's actions would threaten to eradicate the Earth of its sources, leaving it and the inhabitants worldwide to rot. Obviously, Rose wouldn't want anything like this to happen, and rebelled against their own race to protect Earth.
On the thought of harvesting resources, minerals and gems are buried deep into the Earth, which may be useful or a necessity to the Gems, which would be their cause for destroying it. Earth may be a gold mine to them.