However, Minshew said that the results were the same across the board, in different age groups and other demographics.
The findings are part of a shift that's happening in the workplace, she pointed out. For instance, today's labor force is also much more mobile. Of those surveyed, 89% said they would move for the right company or role.
"The factors they're using to define what is the right company or role, it's things like the culture, the values, the employee experience. Sometimes the perks and benefits, as well. Sometimes the company's reputation," said Minshew, author of "The New Rules of Work."
In fact, 85% of those surveyed said a company's reputation is important or very important when they are considering working there. And that doesn't just include the "prestige" of the company, but what employees are saying about it as well on social media and online review platforms.
"Companies used to be able to control their brand and today there are so many ways that your employees are a part of how your brand is perceived in the market," she said.
All this is happening in a tight labor market. The unemployment rate is near historic lows and job growth for March came in better than expected. Nonfarm payrolls grew by 196,000 last month, the Bureau of Labor Statistics reported on Friday. Wage gains increased 0.14% for the month and 3.2% year over year, below expectations.
It all adds up to more job openings than eligible workers to fill them, which gives more power to those seeking jobs. That's why companies should have a clear message to attract the best millennial talent.
"We're seeing today's workforce take a much more nuanced view of where they want to work and then they're voting with their feet," Minshew said.
—CNBC's Crystal Lau contributed to this report.
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