His explanation makes sense. Translation of the last verse but one "Ya salimos de España" = "We already leave Spain": the 1st person of plural of indicative present and of indicative preterit are the same. So, whether it is "We already left Spain" as in Joe's translation or "ya we're leaving Spain" (in present tense, I feel "ya" more as "at last" than as "already"), the war is over.
Letra (sing.) = lyrics (pl.)