The way you handle this as a typical employee is to not work for dicks. That way when they see you being successful they cheer you on rather than try to bring you down.
Also, you don't always have no leverage to negotiate contract terms. When I separated from my last job, my severance agreement as given to me included a 2 year gag clause keeping me from talking about it to anyone. I negotiated it down to six months, using the time-honored tactic of bitching until I got my way.
Bitching is a useful tool in the kind of low-stakes environment that most employee negotiations happen in. Legal action is the equivalent of nuclear warfare, if you're willing to bitch about something, the company, so long as you're not working for a bunch of dicks, is going to eventually open up about what they need to get out of a particular contract clause. This paves the way for a gentleman's agreement whereby you agree to not fuck their shit up, and they agree to not fuck yours up.
In my case, what they wanted was for me to not lead an employee charge for better perks / compensation, and I just wanted to be able to yak about it on Hacker News. So I agreed to keep my mouth shut to my fellow employees about the agreement, and they agreed to reduce the length of the gag clause.
But again, you can't be working for a bunch of dicks. You need to maintain good relationships with your bosses and company leadership and your work output and ethic should never be in question. You are, in other words, loyal to each other. It's great to be ambitious and to want more out of life, but you shouldn't stomp all over the people who are helping you to get there.
Every time I've ever seen one of these "former employer fucked with me after I moved on" stories, the employee in question was clearly working for a bunch of dicks. Your intuition is your most valuable asset as a little guy. Your chances of getting stepped on can range from 0% all the way up to 100% if you're working in the entertainment biz where stepping on little guys is just the culture. You don't have to bury your head in the sand and ignore the risk.