The number of new housing starts has surged in recent months, and the trend is being powered in part by an unlikely bunch — millennials, Sheryl Palmer, CEO of homebuilder Taylor Morrison, told CNBC on Thursday.

Consumers are "changing their relationship with homeownership" and it's evident in the increase of the number of people who are saving, she said in a "Mad Money" interview.

"People are feeling good, and their confidence is absolutely showing in the real estate market, and that's not even to mention the demographic tailwinds we have with how the millennials are feeling about buying their first or second house, and certainly the boomers," Palmer said in a sitdown with Jim Cramer.

Taylor Morrison, which has operations in eight markets including California, Georgia, North Carolina and Illinois, last week announced that it saw a 30% year-over-year increase in housing orders for the months of July and August. Palmer credits lower interest rates and cheaper mortgages for the boost in demand.

The company's shares have risen nearly 10% since Sept. 10.

Palmer said 1 in 3 of the company's buyers are millennials. Five years ago, the generation made up 20% of Taylor Morrison's buyers, she added. Affordability issues are real and vary from market to market, but they are "not as real as I think the media portrays," she said.

"Everyone talks about the millennials like they're just one group of people and they're not buying. We're just not seeing that," Palmer said. "In fact, we're finding exactly the opposite: They're quite qualified."

Taylor Morrison looks at millennials, those ages 22 to 37, as a split generation. About 75% of millennials who are 30 years or older are in the process of buying their second houses, Palmer said.

The home construction firm targets millennials and baby boomers, which she estimated makes up about 166 million people.

"The average age of a millennial wanting to buy is that 32-33 [range] and that's generally directed through marriage — more important, children — and ... they're quite excited," Palmer said. "They want exactly what they grew up with."

In the broader industry, housing starts reportedly hit a 12-year high in August.