EJM has both full managed and charter managed A/C.
Full managed your pay, schedule, everything comes from EJM. You are basically an employee of EJM. You cannot turn down trips.
Charter managed, the airplane is on EJM's certificate, but EJM must call owner for permission to charter the airplane for specific trips, these trips can be turned down for any reason. Pilots are hired, payed, and managed by owner of aircraft and pilots generally consider themselves an employee of aircraft owner rather than EJM.
EJM does alot of trips for NetJets owners, and yes, they are first in line when NetJets cannot fulfill a commitment due to broke airplane or whatever. These trips are flown 135 by EJM.
I would guess that the ad for the EJM pilot is a charter managed aircraft that has that schedule worked out among its current pilots, as far as the travel goes, who knows, I guess the only way to find out is to inquire into the job.