Aleinu between Mincha and Ma'ariv

If I pray privately and I say Mincha and Ma'ariv be'zmanu do I say Aleinu, when I finish Mincha or just after Ma'ariv like in Synagogue?

GBaum

In שלחן ערוך אורח חיים סימן צ סעיף ט the Rema comments that even those people living in areas that don't have a minyan should nevertheless daven Shacharis and Arvis at the time that the tzibbur davens. The Magen Avraham comments (and is quoted by the Mishna B'rura and the Mekor Chaim probably others too) in the name of the Shelah, that "in Ashkenaz where they are accustomed to to push forward Arvis (i.e. daven back-to-back), an individual dwelling in a town or a traveler (i.e. both with no minyan) needs to wait for Tzais HaKochavim (to daven)," If so then if you daven y'chidus you will be davening mincha and ma'ariv seperately, and as such would say Aleinu after mincha, and after ma'ariv. Similar to one who davened in a shul that separates mincha and ma'ariv and does not daven them back to back. Maybe this answers the query?

BAvis

If I were to stay in Shul for the break between Mincho and Arvis (i.e. Shabbos when people eat Seudo Shlishis) would I still say Oleinu after Mincho or only when I leave Shul?

Technically though I would not have to say it, and I can rely on the Oruch Hashulchon.