1 Rainbow Gem will be received upon first clear of each color rush.
This event occurs two times on Monday (and every Friday since 1st of April 2016, too) and lasts 30 minutes each. Today you can chose when to start this event, but in the past (until mod-2016 or so) this event was available at set times each day. This was known as 'Guerrilla Turtles' era. See Guerrilla Turtles Times for historical info on how to calculate the time the turtles will arrive.
The event above is an example of a black turtle rush. Analogous events occur for other four colors. In the past, Black Turtles where most common, usually on each Monday, and Yellow least common.
The first stage contains 5 Treasure turtles, the middle stages, one Daimyo and 2-3 Treasure ones, and the last one, one Elder and two Daimyo. Two special rare stages can appear: one which duplicates the final one, and the best one - containing just the Elder turtle, virtually guaranteeing its drop.