Yes, that is correct; if present the Chairman must chair the meeting. The question implies, but doesn't explicitly say, that the Chair remained at the meeting. The answer lies in the circumstances, was their something mischievous afoot or was it purely innocent. There are times when this would be perfectly reasonable: perhaps the Chair had previously advised of his need to leave the meeting early, or perhaps he had declared an interest in the subsequent item(s).
The minutes would be signed, when approved, by the whoever was in the chair when the resolution to approve them was passed. Not necessarily by anyone who chaired the meeting to which the minutes relate.