Challah, Chapter 3, Mishnah 3. This mishnah deals with dough that was consecrated to the Temple treasury and then redeemed, and with the question of which moment determines its obligation in challah: the moment of consecration, the moment of redemption, or the moment of rolling the dough.
The first two cases - obligated in challah:
"Hikdishah isatah ad shelo gilgelah u'fda'atah - chayeves" - a person consecrated his dough before he rolled it, that is, before it became dough proper, and afterward redeemed it. Even though at a certain point it was consecrated, he removed that sanctity from it through the redemption, and therefore it is obligated in challah.
"Mishegilgelah u'fda'atah - chayeves" - he consecrated it after it had already been rolled, and afterward redeemed it. This too is obligated.
The third case - exempt from challah:
The case in which the consecration prevents the obligation from taking effect is this: "Hikdishatah ad shelo gilgelah, v'gilgelah hagizbar, v'achar kach pda'atah - peturah" - he consecrated the dough before it became dough proper, and it was the Temple treasurer who rolled it while it was still the property of hekdesh. It turns out that the obligation of challah took effect at a time when the dough belonged to hekdesh, and only afterward did he redeem it, and therefore it is exempt.
The difference between the cases is clear: in the first two cases the dough was not consecrated at the moment of rolling - either the sanctity preceded the rolling or it came after it. But in the third case, at the very moment that the dough became obligated in challah it was consecrated, and therefore it is exempt.
In summary: this is the reason the mishnah gives in its closing words - "shebisha'as chovasah haysah peturah" - because at the time of its obligation it was exempt. At the moment when it should have become obligated in challah in the normal way, it was exempt, because it belonged to hekdesh, and hekdesh is not obligated in challah.