Alright, I spent an hour looking at this.
I ran the scroll view example scene which has a center on child. That worked so, the NGUI code is operational.
I made a bare bones scene to emulate the example and see where the issue lied.
Long story short, the Center On Child Component doesn't appear initially active when the game runs, despite showing a checked state in the property inspector. When I unchecked it and then re-checked it, then the Center On Child functionality started working.
So previously in NGUI 3.6.4, the component must have been active from the get go, but something must have changed in between then an 3.6.9 to make it start as inactive.
A work around would be for me to activate it myself on startup, but I am assuming that you will put in a fix for this?