The structure is:
"only" + [adverbial] + [verb with tense] + [subject] + [the rest].
The adverbial is "when that unit is complete", "would" is the verb with tense, and the subject is "you".
A simpler way of phrasing the same sentence is:
You would only begin to think about the second most critical element on the page when the unit is complete.
Other examples of sentences with this structure:
"Only then did she understand her true power."
"Only after the dealer finishes dealing out all the cards should you look at your hand."
"Only with strong medicine can I sleep through the night."
With this structure, as with many others in English, the subject and its verb are switched.
Also read rjpond's answer for info on inverted structures in English beyond just "only...".