Well looking at that link, Nauru did buy out full rights to the phosphate mining in 1970, and they seem to have massively ramped up the extraction after that: they bought the rights for $21 million but then apparently made $100+ million per year selling the stuff. For comparison, back in 1948 the amount extracted was about $750,000 worth. If Nauru bought out the investment for $21 million it would actually make sense that there was about $1 million worth being extracted: 15 or 20 years is about right for the payoff time for an investment. But how did that then turn into $100 million per year of revenue? The only way these figures make sense is if the Nauruans massively ramped up production after they obtained the rights.
Then, when the stuff ran out, they decided to sue Australia for the environmental damages over the whole thing. We settled out of court. But ... going by the raw figures it kind of seems like the massive increase in extraction rates happened after they took control. Additionally they had $1 billion saved up, but that money was lost to corruption and mismanagement. Australia plays some part but they largely did this to themselves. The population of Nauru is only 12000. They could have extracted $10 million worth per year, used that to create jobs and still had the stuff propping up the economy for 200 years.
It's the standard curse of a resource boom and corrupt leadership. Probably the reason they sued Australia was misdirection so that the political class didn't get lynched for ruining the environment then stealing all the money.
As for the John Howard / asylum seeker stuff, which is really shitty from our end, from the Nauru side the only reason to do that is that the top-heavy political class that grew on the back of the phosphate really needed a new revenue source. All of that is nothing to do with taking care of their own people or creating jobs, but about maintaining the gravy train. Considering how few Nauruans there actually are, the government class there is like some kind of souped-up local council who somehow burned through billions of dollars and now they need more to keep their positions. I mean, literally everyone on the island should in fact be quite wealthy now.