Why is that in certain plants deficiency symptoms appear first in younger parts of the plant while in others they do so in mature organs?

The appearance of the deficiency depends on the mobility of the element in plants. Therfore in certain plants the deficiency appears in the younger parts while in other in the mature plants.
If the element is mobile, then the deficiency appears in the older tissues first as the biomolecules in the older tissue are broken down to release the element which is then transported to the young tissues. For example, nitrogen being a mobile, its deficiency appear in senescent or older leaves. 
If the element is immobile then the deficiency first appears in the young parts as the these are not transported from the older tissues. Deficiency of the immmobile element calcium is first seen in young parts.