Montgomery is right about the syntactic breaks except that "until" goes with "then" and "not" negates "until then". The construction is called "clefting", because it extracts the focus constituent from a clause (e.g. "I did NOT do it UNTIL THEN"), converts it into the focus of a new main sentence with BE (cf. Chinese "shì" as a focusing strategy), and leaves the now focusless initial sentence after the new main sentence, in NON-focus position, where it cannot be affected by negation. [Observe that "until then" is both the informational focus AND the focus of negation in "I did not do it until then": "not" negates only "until then", not the rest of the sentence. So, the sentence does NOT claim that you did not do it; only that you did not before a certain time, and then you DID it]. If the original sentence had not been negative, e.g. "I did it ONLY until I got married", the cleft sentence would have been "It was only until I got married that I did it". [Implying: not later than then]. In either case, exactly the same focusing mechanism is at play, the only difference being presence of negation/only operating on the original focus. As a matter of fact, as "I did not do it until then" is usually interpreted with focus on "until then", "clefting" is never necessary. The difference, however, is that IN WRITTEN form the cleft version overtly marks the focus, whereas the non-cleft one is compatible with interpretations in which "until then" is NOT in focus. For example, if I read "I did not do it until then" as /ÁI.did.not.do.it.un.til.then/ or /ai.did.NÓT.do.it until.then/, "I" and "not" are focus, respectively. The pronunciation, of course, removes the ambiguity. If you directly use clefting, on the contrary, "[not [until then]]" is the ONLY possible focus. That's why an apparently periphrastic and "uneconomic" turn of speech has consolidated itself particularly in written English.

The current cut here would be your second grouping, it was /// "not until" then /// that... The middle chunk could be translated into a couple of other ways with generally the same meaning: It was /// only then /// that I did it. It was /// then, and not a moment before, /// that I did it. etc., etc. To really break it down, the base of this beginning of a sentence is "It was then that I did it" -- "not until" modifies "then," clarifying that "it" had never happened before. If you look at the examples above, the first one uses "only" to modify then, and the second uses "and not a moment before" to modify "then."