Vlad never ruled in Transylvania. He ruled in the neighboring country, Valahia. The Cozia Monastery is in Valahia, it did exist in Vlad's lifetime, but is was not fortified and not likely to be use during wars, as the place does not have a real military value. Most likely during wars Vlad would retreat to Poenari fortress, a place not mentioned in the film, but much closer to Vlad's capital than Cozia Monastery.