...the phosphorus is added in small pieces. The first pieces of phosphorus usually react violently, but the reaction soon calms down...
They are talking of pieces of phosphorus. Since the only modification of phosphorus which is sold in pieces, lumps or in the form of sticks is white phosphorus, I think this "antique" procedure works with the white variety.
There must be some reason for the replacement of the air with carbon dioxide in the second article... ::)
Are you absolutely sure they used red phosphorus, is it specifically mentioned in those articles?