Although "sin" does make the object definite and would usually put the adjective between it and the noun into its "e-form", "egen/eget/egne" and "anden/andet/andre" are exceptions to this rule
So "egen" and "anden" get the "form" of the noun (like a t-form before a t-word, the n-form before an n-word, like in an indefinite situation) even after sin/sit/sine?
Yes, it also works with all possessive pronouns ("Mit eget hus", "hans egen bil") and in the case of "anden" it also is true with the definite article ("Den anden pige", "Det andet dyr")