The only reference I can find is from Miller [M] who shows the labels as havuing been manufactured in Germany by Homophon gmbh, and sold in Australia between 1912 and 1914, probably by British Record Pty Ltd.

See also Rexophone, also made by   Homophon gmbh.

Records in collection:

L037 sc3 RONDOPHONE RECORD  Recorded in England, Pressed in Prussia.
Cat. No. 1191 (60569) THE LEA RIG.  Violin Solo by Mackenzie Murdoch with Piano accompaniment.
Cat.No. 1191 (60570) ISLE O; SKYE   Ibid.   [I'd regard this as a British record as that is where it was presumably released, even though [ressed, ie manufaactured, in Prussia.]

L068 sc3 RONDOPHONE RECORD Pressed in Berlin.
60670 (K110).  THE SONG THAT REACHED MY HEART.  Frank Reed.
60671 (K110).  JUST ACROSS THE BRIGDE OF GOLD  Ibid.  [Should that be 'Bridge'?]