It's Just A Job
While doing your job with 110% effort is great, at the same time you need to take it for what it is. You are only there 4-8 hours a day, 20 hours a week. Then you go home. You are ultimately responsible for how you treat customers and how well you follow through on supervisors' instructions. You have no right to boss people around or yell at them. If you have an issue with them, nicely talk to them or talk to one of the managers. You also have no right to accuse other people of being mad at your promotion when you don't even know. Stop assuming that everyone is stupid and doesn't know what they are doing. Newsflash: a lot of people there have worked there longer than you!
(If you haven't already figured out, this is directed towards a co-worker who's starting drama)