There's more to the story than that. Prepositions behave differently than adverbs. ἔξω can appear just about anywhere. Clause initial, clause final. In front of a finite verb while joining with a case that follows the verb. In other words the finite verb can separate ἔξω from it's substantive. You won't find that very often with regular prepositions.
I went looking for a pattern: ἔξω + finite verb + genitive case substantive
I also noticed a pattern: genitive case substantive + ἔξω + finite verbEuripides Trag., Iphigenia Aulidensis Line 863
{Αχ.} ὡς μόνοιν λέγοις ἄν, ἔξω δ' ἐλθὲ βασιλείων δόμων.
2Clem. 7:4 εἰδέναι [12] ἡμᾶς δεῖ, ὅτι ὁ τὸν φθαρτὸν ἀγῶνα ἀγωνιζόμενος, ἐὰν εὑρεθῇ φθείρων, μαστιγωθεὶς αἴρεται καὶ ἔξω βάλλεται τοῦ σταδίου.
This is obviously not an exhaustive study of the issue.Sophocles Trag., Oedipus tyrannus Line 622
{ΚΡ.} Τί δῆτα χρῄζεις; ἦ με γῆς ἔξω βαλεῖν;