Only the City Council can appoint the City Auditor; the appointment must be made in a properly noticed meeting held in accordance with the State of California's open meeting law, the Ralph M. Brown Act; and the compensation for this position that is not represented by a union must be determined in an open meeting.
The City Auditor who is leaving employment lacks the authority to appoint his own replacement, because the position of City Auditor is defined in the City Charter as a Council Appointed Officer.
The City Council has not held a properly noticed meeting with an agenda item for the appointment of an Acting City Auditor.
The City Council has not held an open meeting to set the compensation of an Acting City Auditor.
The City Council did hold a Closed Meeting on September 5, 2013, to discuss "Public Employee Performance Evaluation (Exit Review), Title: City Auditor", but that agenda description had nothing to do with the appointment of an Acting City Auditor.
The fact that the September 12, 2013, press release fails to state who appointed Acting City Auditor Boussina, but simply contains a quotation from City Auditor Pelletier, rather than from the Mayor who is the authorized representative of the City Council that is the only legal appointee authority, indicates to me that somebody in City Hall knows that proper procedures were not followed for this appointment.
September 5, 2013, City Council agenda: Web Link
September 12, 2013, press release: Web Link