I believe the term "double negative" refers to a different kind of, erm, double negative (DN). The kind of DN that usually baffles English L1 speakers learning Spanish is the one involving negative pronouns like nadie, nada, ninguno, etc., such as in
- No llegó nadie. ("Nobody came.")
- Decidimos no decir nada. ("We decided not to say anything.")
- A ninguno le tocó nada. ("No-one got anything.")
In this case, however, the expression hasta que no has, believe it or not, the same value as hasta que, i. e. the word no means nothing, although it does add a certain connotation. There's an article on hasta que no in Wikilengua discussing this curious phenomenon. Summarizing it:
- Hasta que no is equivalent to mientras no or en tanto no (in English, "as long as… not").
- The "reasoning" behind this weird usage is that hasta is semantically related to mientras (English: "while", "as long as").
- The language authorities acknowledge the presence of this structure in literary writing and do not condemn its use.
- The no after the hasta que is an expletive; it only reinforces the meaning.
- In Latin America it's more common to say hasta que followed by the affirmative. [This I'm not sure of.]
- Also in some dialects in Latin America the converse phenomenon sometimes takes place, where people omit the negative in expressions like Hasta las cuatro iré. This literally reads "I will go until four", but it means "I will not go until four". It sounds rather weird to the rest of us.
So, as you surmised, your example is indeed a case where hasta que means "if" (or "while"). Other examples:
"¡No habrá comida hasta que no puedan levantarse y trabajar!" (J. R. Ribeyro, "Los gallinazos sin plumas")
Meaning: "There won't be food until you can get up and work" or "There will be no food while you can't get up and work".
"El chino hasta que no se siente amigo tuyo no hace negocios" (La Nación, Argentina)
Meaning: "The Chinese, until they feel they are your friends, won't do business" or "The Chinese won't do business while they don't feel they are your friends".
"Hasta que no se firme el acuerdo no se levantará el paro" (El Espectador, Colombia)
Meaning: "Until the agreement is signed the strike won't be lifted" or "The strike won't be lifted while the agreement has not been signed."