I have this question and I can't seem to find any sources which I can used to determine a potential answer.
For a traditional foundry sand mold ; the metal freezes as essentially the size of the cavity but then shrinks as it cools to room temperature. So the cavity is larger to accommodate this shrinkage. For a permanent mold or die casting it is similar except the metal die is warm>hot so when it is machined at room temperature , the expansion of the warm die and the shrinkage or the part must be considered. Then there are more complicated situations like investment /shell casting. A plastic pattern is made by injecting into a warm die > the plastic shrinks to room temp . The plastic is embedded in ceramic > the ceramic is heated to high temp ( eg. 1600 F) and expands > the metal is poured in and freezes at about 1600 F then shrinks down to room temp. Experience helps in determining what size the die cavity for the plastic part should be at room temp.