Yes, exactly.

https://en.m.wikipedia.org/wiki/Interactive_voice_response

That's what they are called in India, at least, where I live, and where I am from, although the term would not have originated in India, since it would have been brought in by mobile phone companies.

https://en.m.wikipedia.org/wiki/Interactive_voice_response

Although I have a good amount of exposure to, and familiarity, with US terms and slang, due to older relatives up to grandfather level having visited the US for more than short periods, having visited the US myself, and having worked in US-based companies (but in India), the exposure is not complete, that's why I was not familiar with the term phone tree.

That should not be surprising to anyone.