How does the parenthetical "that is" function?

It's the last sentence of an article in The Economist.

Some of the powerful elders might have faded from the scene. Mr Xi and Li Keqiang might then have a freer hand to promote their own people, and perhaps more daring ones. If, that is, they manage to keep control until then.

I know the whole sentence means "it is possible only if they manage to keep control" or "it's impossible unless they manage to keep control". But I don't understand how it functions.

Question 1: What does "that" refer? Or is it just an empty word refering to nothing?

And I also have a question about the reference of "it" in "It is not until 3am that they returned home." I think "it" refers to the fact that "they returned home", and the sentence can be restructured as "the fact that they returned home is not true until 3am." Though it sounds wierd, but it helped me to understand how "it" functions. But some people tell me "it" doesn't refer to anything in that sentence, and I shouldn't comprehend it that way.

Question 2: Am I really wrong in the understanding of "it" in that sentence? If so, how do you think I should understand it?

Supplement:

So everybody thinks that is is short for that is to say? But I really think it would be anything but that is to say. Before I asked this question I tried to comprehend it that way, and here came an absolute logical error: since that is to say usually connect two sentences expressing a similar meaning, the two sentences should be in the same type of pattern. That is to say, if the previous sentence is a statement, then the following one should be a statement as well, despite all the clause and parenthesis. But the sentence I quoted is just a conditional clause, and its previous sentence (sorry for not having quoted it earlier) is a statement.

I strongly suspect that that is was coined as a literal translation of the Latin expression id est (i.e.) with the same meaning, because the construction makes more sense in Latin.

Originally, that is (to say) was used at the beginning of a sentence, where that referred to the previous sentence, or between the two sentences, just like i.e.:

The first Roman Emperor was Gaius Julius Caesar. That is, he was the first man who ruled the Empire de facto single-handedly, though he was no emperor in name.

In later use, its position has tended to shift around a bit, but it still refers back to the previous sentence or an idea expressed therein.

Your analysis of it is perfectly fine. You could say it is the subject and the that clause an appositional complement to the subject.

This did not happen until 3 am, (namely) the fact that they returned home.

It is of course a fixed idiom, so that the internal structure doesn't matter a great deal any more. Note that it is used in many languages, like French c'etait là que..., Dutch het was daar dat... = "it was there that...".

A previous statement is made. It is given the follow-up statement that indicates the statement is only possible if another condition occurs.

I'm going to the movies tonight. If, that is, my car ever gets out of the shop.

If, that is, they manage to keep control until then.

The that is a pronoun referring to whatever is stated earlier, probably immediately prior in the previous sentence. The placing of "that is" after if serves to emphasise the "If" and the improbability (in the author's view) that they will "keep control until then".

It was not until 3am that they returned home.

Here the it is a dummy which is there to provide a subject for the verb. It's the complement which is important — they did not return home until 3am. It in that sentence does indeed mean nothing, and the sentence has a similar (but not absolutely identical) structure and analysis to "It is raining".

That is (to say) is used to give more details about something, with that referring to whatever was just said and with an elaboration following the phrase.

Pronouns do not always refer to something else identified in the text.

Sometimes pronouns are exophoric and refer to something extralinguistic:

That is John's. [Speaker points to a book belonging to John, establishing a referent.]

Sometimes pronouns are homophoric and refer to something known only through context:

He is risen. [Spoken in a Christian church, establishing the referent as Jesus.]

Sometimes pronouns are expletive, or dummies, and have no referent. They are required by functional syntax have no semantic meaning.

There are seven continents. [The usual way of stating 'Seven continents exist'.]

Finally, some pronouns appear in idiomatic expressions and have no referent but contribute to a construction that has semantic meaning:

John was really out of it. [In the sense of 'John was dazed and confused'.]

In this last case, it is not fruitful to ask "John was out of what?". There is no referent for the 'it' in 'out of it'; 'out of it' is a construction with a meaning of its own. The same situation applies to 'that is' in the sense of 'i.e.': there is no referent for "that", it's just part of the phrase.