No, after the eggs hatch...about two to three weeks after they are laid...the tiny fish larvae enter the sea of plankton (tiny to microscopic, plant and animal 'drifters') and are swept up by the prevailing currents. As 'drifters' they are transported to other areas never to be seen by the parent again. When they grow big enough to be able to swim by themselves they find their own territories in which to live.
If you've answered all the questions, you now should have a better understanding of how the whole picture works. The female finds a suitable male. She deposits her eggs on the algae mat in a clump, then the male releases his sperm over the eggs to fertilize them. Then the female garibaldi moves on to lay more eggs at another nest of her choice, and the male stays and guards his nest and clumps of eggs until they hatch and the tiny fish are carried away in the current.