Calliope paid more attention to the strange man now as he left, eyes narrowing very slightly as her quick mind tried to work out who he was. If he was anyone of this much import, he was probably Melpomene's ex. She knew they'd parted on bad terms, but apparently childbirth was enough to bridge some of the gap.
Apollo was stating who would be here to look after Melpomene though, that proprietal "we" ringing quite clearly to Calliope's ears. She kissed her sister's head, turning her focus back. The man wasn't a priority right now.
Honestly, if Apollo wasn't a healer, she'd be sending him out of the room too. Birthing was women's business. She looked around at him. "Can we get some gas and air in here? Something to take the edge off her pain?" she asked, respectfully but firmly that this should happen very soon.