Yes. It can mean the same as when, and it does in your reference sentence.
We can replace now that with when, and the meaning is clear and essentially the same.
But there is a slight difference: Now that explicitly conveys the information and we now are adults, whereas, of course, when does not always carry such meaning.
And, while the context makes clear that a past cause is being connected with a current consequence, when does not necessarily do that in other contexts, while now that does.
It rained when I went on vacation last year.
We can't replace when with now that here, of course, which is why dictionaries and people are reluctant to say now that means when.
Now that it's raining, I'm going to open my umbrella.
We can't replace now that with when in the above. It changes the meaning. Note that it signals a causal relationship.
Just to restate my answer in another way:
How did our diets back when we were children affect whether we are obese at the present time when we are adults?
We can omit at the present time in the above, and it makes sense, so we may be tempted to say that it means when. But it leaves out the fact that we are adults now.
Given that we understand that as implied or assumed, then yes, we can say that in this sentence, it means when.
Oxford's "recently happened or is happening" idea may be misleading: "The land bridge between Alaska and Asia has disappeared now that we've exited the Ice Age", for example, technically fits, but may not follow intuitively from that description.
... now that does not convey the result of being adult
Now that introduces the event or situation or characterization of the time period that marks or attends the result: attaining adulthood.
Its relationship with cause or effect is not so simple as it conveys a result.
Now that the holidays are over, I feel somewhat bored.
I'm very nervous, now that you mention it.