ὁ μὲν οὖν Κῦρος ὡς ἤκουσεν, ἀναπηδήσας ἐκ τῆς ἕδρας ὑπήντα τε αὐτῷ καὶ ἐδεξιοῦτο:
why imperfects? I would expect aorists.
There’s a very similar instance in the Anabasis (1.8.3): Κῦρός τε καταπηδήσας ἀπὸ τοῦ ἅρματος τὸν θώρακα ἐνεδύετο καὶ ἀναβὰς ἐπὶ τὸν ἵππον τὰ παλτὰ εἰς τὰς χεῖρας ἔλαβε. There was an earlier thread on that entitled “Aspect Qujestion”(sic), and it is, of course, a matter of aspect. This meet-and-greet episode was evidently not instantaneous.
I would think that the emphasis in both of these examples is on incompleteness of the imperfect acts, rather than respective durations of the aorist versus imperfect acts.
Looking at the paragraph in the Cyropaedia, the imperfects to me clearly show that the ἐκπεπληγμένοι ἦσαν is happening while Cyrus is still engaged in greeting the φύλαξ. Notice that after encouraging the others (the ὑπηρέται, I guess), he gives them his speech of encouragement, and then they all greet the φύλαξ too.
In the Anabasis scene, the incompleteness (and therefore continuance) of Cyrus’s equipage action is famously important for what comes next.