Found on the KIX website
http://www.kansai-airport.or.jp/english/qanda/index.htm

Transit at KIX
Q: I'm going to transit at KIX. Do I have to pay the PSFC (Passenger Service Facilities Charge)?
A: The PSFC is required unless your connecting flight departs Kansai airport on the same day of your arrival. If you qualify, you need to get a "Certificate for Exemption/Deferred Payment of PSFC" from airline companies to be exempt from the charge. Please also note that the exemption rule does not apply to passengers coming from any domestic airports.