Compare four cases:
الرَّجُلِ: no tanwīn due to al-, but ordinary genitive kasra.
كِتَابِ زَيْدٍ: no tanwīn on the muḍāf, though it has genitive kasra.
هَذَا: an indeclinable demonstrative with positional case.
أَحْمَدَ: a diptote, without tanwīn and with genitive fatḥa in the relevant form.
Use cause + syntactic function + case marker, not the lack of tanwīn alone.