SYDNEY, Australia — Atlassian is a very boring software company. It develops products for software engineers and project managers, with hits like Jira (for software project management and bug tracking) and Fisheye (a revision-control browser). And who could forget Confluence (an enterprise knowledge management system)?

So why are its two founders household names in Australia?

Because Scott Farquhar and Mike Cannon-Brookes, both 39, are the country’s first start-up-to-I.P.O. tech billionaires. And because in the last year, they have started to make noise.

Until recently, they largely stayed out of the public eye, even as Atlassian grew to become a $20 billion company. Now, as Australian politics tilt toward the right on global issues like immigration, cybersecurity and climate change, they are emerging as new political voices, getting in Twitter spats and lobbying Parliament.

The other reason they are now household names: In 2017, Mr. Farquhar bought the most expensive home in Australia, a historic Sydney estate that sold for 73 million Australian dollars, or $52 million.