This is not unique to the pronunciation of autophagy
There is no principle saying that the pronunciation of a word must always divide it into parts that correspond to its etymological components. That's just the way compounds formed in English from English words (like paperhanger) tend to be pronounced. But not all compounds are formed in English from English words.
The pronunciation /ɔːˈtɒfədʒi/ for autophagy follows a very common pronunciation pattern for Greek-derived compound words ending in -y. I describe it in my answer to the similar previous question Pronunciation of tetrameter, pentameter, etc. There are scores of other words pronounced like this, including biology (and -ology words in general).*
Sometimes multiple stress patterns are possible for a word like this
For certain words of this type, it seems to be somewhat common for some speakers to use the stress pattern of English compound words instead. For example, the John Wells quotation in my linked answer talks about "cardiologists, cardiac surgeons, paramedics and nurses" using the pronunciation /ˌθrɒmbəʊˈlaɪsɪs/ for thrombolysis. My high school chemistry teacher used the pronunciation /haɪdroʊˈlaɪsɪs/ for hydrolysis: she was aware of the pronunciation with stress on the second syllable, but consciously chose to pronounce it with stress on the first and third syllable in the classroom to emphasize the etymology/structure of the word in her lectures.
The pronunciations of rare scientific terms are often not as fixed as the pronunciations of other, more common words. Many scientists don't care that much about pronouncing things according to a system, and the ones that do care about it don't all agree about what the system should be. I wouldn't expect anyone to start pronouncing biology as /baɪoʊ.loʊdʒi/ or astronomy as /æstroʊ.noʊmi/, but it seems more plausible that some scientists might use a pronunciation like /ˈɔːtoʊˌfeɪdʒi/. You'd have to listen to find out; I found what seems to be one example through Youglish: https://www.youtube.com/watch?v=9AA7akJ21ZI&feature=youtu.be&t=493
*Side note on syllabification
The syllabification of words like this is actually a bit of a controversial issue in linguistics. Some linguists would say that /ɔːˈtɒfədʒi/ and /baɪˈɒlədʒi/ are divided into the syllables /ɔːˈtɒ.fə.dʒi/ and /baɪˈɒ.lə.dʒi/. It's clear that English words tend not to end in vowels like /ɒ/, but it's a little less obvious that this restriction applies to stressed word-internal syllables.
If we consider the stressed syllable to be /ˈtɒf/ rather than /ˈtɒ/, the explanation would be either that stressed syllables in English tend to "capture" adjacent consonants, or that stressed "short vowels" in particular tend to "capture" a following consonant.