In contrast to fathah tanwin, ordinary dammah tanwin and kasrah tanwin lose their n-like sound in a pause and leave the final consonant still. They do not acquire the new alif length associated with ordinary fathah tanwin.
«كِتَابٌ» — with dammah tanwin in connection, but still final ba at a stop and no added alif.
«بَيْتٍ» — with kasrah tanwin in connection, but still final ta at a stop and no extra alif.
«رَحْمَةً» — a fathah-tanwin word ending in ta marbuta follows the characteristic stopped ha ending, not an unqualified generalization of the alif rule.
The correct decision therefore considers the type of tanwin and the form of the final letter together.