I have a cinnamon mauve female budgie which is paired with a double factor yellow spangle male. Now among the three chicks, one is blue spangle and other two are Red Eyed lutino. I have paired this female with another mauve male before and that time the chicks were either cinnamon mauve male or opaline mauve female. Now, from a DF Spangle, all the babies should be spangle. So, is the lutino babies are actually spangle but masked due to their ino mutation? Will they be all female and the father is causing the ino gene?

Yes, all babies will be spangle. The ~inos will be masking it and will be females. Dad is passing on the ~ino gene.