The Puppeteers had to make some drastic alterations to their home system, during their history, as global warming and overindustrialisation was rapidly making their planet uninhabitable. They moved their planet further from their sun, to lessen the effects of global warming, but overindustrialisation forced them to move four of the other planets in their system closer to their world and terraform them into "farming worlds", arranging the five planets into a Klemperer rosette.
"I had explained," said Nessus, "that our civilisation was dying in its own waste heat. Total conversion of energy had rid us of all waste products of civilisation, save that one. We had no choice but to move our world outward from its primary. It was very dangerous. There was much madness that year. For that reason it is famous in our history. But we had purchased a reactionless, inertialess drive from the Outsiders. You may have guessed their price. We are still paying in installments. We had moved two agricultural worlds; we had experimented with other, useless worlds of our system using the Outsider drive. In any case, we did it. We moved our world. We found that a sun was a liability rather than an asset. We moved our world to a tenth of a light year's distance, keeping the primary only as an anchor. We needed the farming worlds and it would have been dangerous to let our world wander randomly through space. Otherwise we would not have needed a sun at all. We had brought suitable worlds from nearby systems, increasing our agricultural worlds to four, and setting them in a Kemplerer [sic] Rosette." —(From Ringworld, Chapter 5, published 1970.)
Eventually, their sun converted from a yellow dwarf to a red giant, so the Puppeteers moved the "Fleet of Worlds", the five planets, to their system's Oort cloud. This is one of the reasons the Puppeteers were so successful at keeping the location of their homeworld a secret — explorers would be looking for a yellow dwarf (as one could surmise that Puppeteers had evolved around a yellow dwarf from their biology and that they were comfortable on Earth-like planets without pressure suits) when their planet(s) were actually near a red giant.
Beowulf Shaeffer, five years after his discovery about tidal forces, discovers that the Galactic Core is exploding. This news prompts the Puppeteer Exodus, where the Fleet of Worlds flee the galaxy at just under light speed for the Magellanic Clouds, in the hope that by the time the explosion reaches the Fleet of Worlds, the Puppeteers will have found a way to protect their civilisation. This exodus prompts a major stock market crash in human society; in 2864, the Fleet of Worlds leaves Known Space.
It should be noted, however, that the speed at which the Fleet of Worlds is moving (0.8c) would cause nearly as much damage as the Core explosion itself. This means that the Puppeteers may, in fact, have a means to deal with radiation affecting entire worlds. In "Crashlander" it is speculated that the Puppeteers are planning on moving to the uninhabited Core, isolated from potentially dangerous species (one would think that Louis Wu would have noticed this when flying there on the Long Shot in Ringworld). "Crashlander" also reveals that the Puppeteers may have feigned their ignorance of tidal forces.