A general rule of thumb (for any words) is that on'yomi tends to go with on'yomi and kun'yomi tends to go with kun'yomi.
じんぼう is on'yomi and おおて is kun'yomi, so matching the on'yomi of ちょう with the former and the kun'yomi of まち with the later has a natural feeling to it.
There are exceptions though. In Osaka there is an おおてちょう. It uses the same kanji as the one in Tokyo, it just uses the on'yomi instead of the kun'yomi. So you can't predict them perfectly.
There might be reasons for places choosing one or the other, or there may be no deep reasons. The existence of these "same exact kanji but different readings" place names like おおてまち and おおてちょう shows that there's no hard rule to follow. You should just expect weirdness from place names.
That makes sense. Thank you!
What determines how 町 is pronounced?
I've often wondered why 町 is pronounced "machi" in Otemachi and "chou" in Jinbouchou. They are both considered districts of Tokyo, next to each other. Can anyone out there shed some light on this for me?