I live nearby...sort of. Orange Co. Most of the shopping areas are owned by the Irvine Co. and there is no riding in the lot. Lots and lots of kids riding bikes here and I would rather they wouldn't ride in the parking lot anyway. You never know. Besides, its illegal to ride on the sidewalk anyway. And if it is private property, its private property. I ride my bike to Ralphs all the time and once in while, they'll ask me to "kindly walk" my bike. Perhaps it was just the way the guard talked to you? I hate that when they think they have so much power...just a guard.
My kids remind me all the time to "dad! get off you bike" when we are in the shopping plazas.