Currently, is inflation being effectively managed by central bank rates?

I listened to a podcast about the Australian economy, where the economist suggested that currently inflation in Australia is not responding as expected to interest rates. He attributed this to a generational effect where a large population of older people (obviously not all older people) who have a lot of spending power and no loans, who are just continuing to spend as they did before.

Despite that, I don't have the knowledge to assess whether the economist is right, although I don't believe that the reserve bank actually has any other measures to use to affect inflation. If he is right about the cause then I guess taxation would be the normal remedy. That said, I assume that inflation is generally effectively managed by rate changes in countries with effective central banks, but with perhaps some present minor variations.

So my questions are:

• Currently, is inflation being effectively managed by interest rates in an expected manner in countries with appropriately independent, empowered, and apolitical central banks?
• If Australia's inflation isn't being managed by interest rates, what can realistically be done about this?

I'm not strictly after answers about Australia, although welcome comment from people with a better perspective than myself, and please do help me understand if I have used a concept incorrectly.