Deutsch is building a Hispanic unit called DLAtino in Los Angeles by poaching a partner and an exec creative director from independent Hispanic shop Grupo Gallegos. Before the move a few months ago, Montse Barrena and Juan Pablo Oubiña, born in Spain and Argentina respectively, had only worked at U.S. Hispanic ad agencies.

At their former agency across town, John Gallegos is going in a very different direction. His recent hires include non-Hispanics Chief Creative Officer Marty Orzio and Chief Marketing Officer Jennifer Mull, as well as a British group account director, Rachel Gilmour, who joined from BBH London. Before Grupo Gallegos, they had only worked at general-market agencies.

This tale of two agencies highlights a move many shops are making to thrive -- or even survive -- in a fast-changing market. Today's growing population of influential, multicultural Americans are too big for general-market agencies to ignore, and fewer are the Spanish-dominant immigrants who were once Hispanic agencies' main targets.

"If you're a regional account in California, you should be ashamed of yourself if Hispanic isn't at the center of everything at the strategy level," Ms. Barrena said.

More Coverage >>

Her move to Deutsch "was about having a seat at the table from the beginning, and not having Hispanic be a tactic at the end, or having to break it to a client that this strategy isn't going to work for us [Hispanics]. It's not about Spanish or English anymore. It's about 'Where do we reach this consumer and where do they consume their content?'" At Deutsch, her goal is to introduce Hispanic into planning at every step, she said.

So far, DLAtino has worked with a few Deutsch clients. Hispanic millennials were a target for a 7Up effort that partnered with seven DJs at seven events last year using electronic dance music, a type of music that wasn't specifically Hispanic, like salsa or merengue, but overindexes among Hispanic millennials.

For Grupo Gallegos, Mr. Gallegos said, "We need to bring in the best talent that believe in the vision that to understand and deliver the total market you must embrace the multicultural audience, if you truly believe they represent the future."

Grupo Gallegos is a key player for longtime clients like the California Milk Processor Board. To get Californians to drink more milk, you have to talk to Hispanic moms.

Mr. Gallegos said senior marketers really only care about demographics that are actionable and grow their business—he displays them on a chart with two simple pyramids. One reflects traditional sales from the current population: 17% Hispanic on top of the broad base of the general market. The other is based on future growth and is reversed, because 89% of the population growth for the six-to-34 age group between 2014 and 2019 will come from Hispanics. "If you look at growth, the pie chart flips," he said.