The successor rate is the fallback rate plus the spread adjustment. There is usually a gap between LIBOR and the fallback rate, and switching without adjustment would give one party a gain and the other a loss, so the adjustment closes that gap. Because the spread adjustment stays fixed after the switch, however, it cannot remove the transfer of value completely.
The spread adjustment for 6-month yen LIBOR was fixed at 0.05809%. Consider a hypothetical example in which TONA compounded in arrears is 0.10000%. The successor rate is 0.15809%.