I don't know about Mexico to Chile. The information that I have says both Santiago and Valparaiso, Chile. I know his uncle Jacinto Acuna also came north and his naturalization clearly states that he was a native of Valparaiso, Chile. All the censuses say that Joseph was from Chile. We have several family letters written from Maria Luisa Acuna in Valparaiso, Chile to Joseph Rumaldo Acuna. Maria Luisa is Joseph's sister and she mentions two other sisters, Maria and Adela. Jacinto's wife is Josephina. Apparently Jacinto and Josephina were married in Chile prior to coming to California as Maria Luisa talks of her as if she knows her intimately. We do have one quirky letter from Maria del Socorro Contreras written to her son, Juan Acuna in Sacramento, Californi dated 1909. It was sent from Chilchota and the only Chilchota I can find is in Mexico. SO there may well be a Mexican link that I haven't yet found.
Does any of this sound like your family? I'm so anxious to know!!!