I am a Romanian born and I currently live in US. I can tell you 100% sure that the names are absolutely Romanian. Dionisie it's a very commun first name in Romania. It comes from the Greek god Dionysos- the god of wine. Romanian are 98% Greek Orthodox, and having Greek orthodox first names it's another way to fight the Catholic domination in Transilvania back then.
Transilvania and Fagaras were part of the Austro-Hungarian Empire, but the Romanian population was always majority. This was up to 1918.