It cannot be said with absolute certainty that both the cistern and bath were simultaneously built by Stephen the Parakoimomenos mentioned in the Patria.
Sources
De insidiis (148) of Constantine VII Porphyrogenitos (r. 945-959) tells of Maurice's flight after Phokas is elevated as the new emperor: ἦν δὲ μετ’ αὐτοῦ καὶ Στέφανος ὁ βαΐουλος Θεοδοσίουὁ κτίσας τὰ Ἁρματίου καὶ τὸ Σάγμα ("And with him [Maurice] was also Stephanos the tutor of Theodosius [Maurice's son], who erected ta Armatiou and the Sagma.")
The Patria repeats similar information that this Stephanos' name can be connected to building activities at Ta Lausou, but it further specifies that it concerns a bath.
Why Crow et al., 2008 describe Ta Armatiou as a cistern is not entirely clear.