Every staffed Amtrak station has at least one full time Amtrak employee assigned to it, usually two of them if the station is open seven days a week. In addition to the two full time employees usually required for a seven day a week operation for one daily train in each direction, each staffed station usually has one guaranteed extra board position. The person in that extra board position can be assigned to one or a handful of stations if there are several staffed stations nearby (such as in the SF Bay Area). In rural areas the extra board employee only has one station to report to and is guaranteed 40 hours of pay each week regardless of whether they are called to work or not, and they are not called in unless one of the regular full time employees is sick or on vacation. It is a pretty sweet job, but the extra board employee must remain on call around the clock and ready to report to work within an hour of being called.
Amtrak full time employees are paid by the hour, per their union contracts, and are paid overtime for late trains that require them to stay after their assigned shifts. This is a big waste of money on some routes like the Sunset when the train will be arriving 8 hours late and an agent has to show up and staff the station beginning at their normal shift time and then stay late for the train. You will notice that most rural stations are open 8-10 hours a day, even for once daily in each direction train service. These are the assigned hours for the employee; hopefully the train(s) will arive within that time and the employee will not have to stay later.
I am not sure exactly how the Chico station operations work, but if the station is open when the Coast Starlights arrive I would assume that it is opened and closed by a caretaker. Greyhound operates a limited hours ticket office in the station (8a-2p and 6p-8p or something like that) so they take care of opening and closing it during the day. Have you been down to Chico at night when the Starlights pass through to see if it is indeed open? A few miles up the line in Redding, California the station is opened by a hired security guard/caretaker from 1am-6am daily for the Starlights, so I would assume Chico is similar.