No need to earn or decrease Caesar's reputation until you go see Benny in The Tops in the Strip. kill Benny or make him flee, and get out of The Tops. and Vulpes Inculta or other person(I can't recall his name, sorry.) will make a comversation with you. then you can get a quest and go to the Caesar's camp. carry out quests from Caesar and the other members. you can get some quest from Vulpes Inculta, Lucius, and Antony.
EDIT: Yep, ive done all that and my rep with them is liked, and has been for ages, but i still havent had a disguised legion spy come up to me and tell me about the boxes. also, if its of any significance, i killed vulpes inculta after he gave me the mark