"We talk about their family and what's happening in their lives," said Velazquez, a certified public accountant and wealth manager for Glendale, Calif.-based US Wealth Management. "We have a cup of coffee or a drink, and an hour into the conversation we still haven't talked business—but we have taken the time to cement that relationship, and that's a necessary precursor to doing business."
Velazquez finds that paying close attention to what makes his clients comfortable gets things off to a positive start, in contrast to counterparts "who tend to get down to business too quickly." Advisors who hope to appeal to an increasingly diverse consumer base must learn to embrace cultural differences and hone their interpersonal skills accordingly, he said.
Velazquez isn't alone in recognizing the opening financial advisors have to appeal to an increasingly diverse population that includes a growing number of residents who have roots in foreign cultures.
(Read More: Female Advisors Know What Women Want)
The Financial Planning Association "is witnessing a growing trend in financial planners seeing the opportunity to develop niche businesses that cater to diverse client's needs, including non-American born individuals and families," said Lauren M. Schadle, executive director of FPA, which is in Denver. "It is more important than ever for financial planners to understand their clients' cultural norms and personal background so they can develop meaningful and long lasting client relationships."
At the same time, a study released in December by the State Farm Center for Women & Financial Services at the American College of Financial Services suggested that financial advisors "increase marketing attention and outreach" to minority women, "whose continued growth in numbers and affluence present advisors, and the industry, with attractive and underserved markets for many years to come."
Meanwhile, larger financial services firms are also stepping up marketing efforts to tap into fast-growing ethnic communities.
(Read More: The $27 Trillion 'Generation D' Investor Prize)
For example, MetLife recently created a Chinese Dragon Boat Game featuring its trademark Snoopy mascot specifically for its Mandarin-language website, and discount broker Charles Schwab promotes "Chinese-speaking financial consultants" online.
There's good reason for advisors to evolve along with the nation's cultural constituency.
In 2011, the population was 16.7 percent Latino and 5 percent Asian, according to the Census Bureau. The latest data show that the U.S. has some 40 million foreign-born residents, making up 13 percent of the population—an increase of 30 percent since 2000.
With a median household income of $66,000 in 2010, Asian-Americans rank higher than the overall U.S. population at $49,800, the Pew Research Center has reported. They also recently surpassed Hispanics as the largest group of new immigrants, the center said.
Financial advisors hoping to work with first- and second-generation immigrants face a number of hurdles, including communication and language barriers.
"Financial planning concepts can be challenging for foreign clients," even those fluent in English, said David Roberts, managing director of WTAS, a San Francisco-based tax and financial advisory firm with a large foreign-born client base.
For example, the commonly used trust fund, in which one person manages an account for a designated beneficiary (such as a spouse or child) doesn't exist in Latin American countries.
"You need someone who is able to articulate how these products work in a way the client can understand, and if the advisor speaks Spanish, that can make a big difference," Roberts said.
As the population becomes more diverse, many financial services firms—specially those in gateway states like California, New York, Texas and Florida—are recruiting a global mix of bilingual specialists.
"We have found that there is a subset of foreigners who are more comfortable dealing with people who understand their cultural differences and speak their native language," said Roberts, adding that his office has designated desks to serve clients from China, India, Latin America and Russia.
The Asian-American market offers immense opportunity, "but it's not one that just anybody can grab," said Winnie Sun, managing director of Sun Group Wealth Partners in Irvine, Calif.
"On the surface, it looks like we've assimilated very well to American culture, and in many ways we have," she said. "But that doesn't change the fact that we would often prefer to work with people who look and sound like ourselves," said Sun, who speaks fluent Chinese. "There's an unspoken comfort there."
She and her business partners, who are Korean and Thai, were recruited heavily by the leading financial advisory firms in Los Angeles when they left their former employer to hang their own shingle, Sun said.
"Every firm wanted us, and they weren't shy about letting me know I was an attractive candidate as a young, female Asian," she recalled.
Louis Barajas, a certified financial planner in Santa Fe Springs, Calif., and author of five books, including "The Latino Journey to Financial Greatness," said the financial services industry has become far more proactive about courting diverse clients in the last 10 years. Nearly 150 independent advisors assembled earlier this year for his cultural sensitivity seminar, hosted by the College for Financial Planning.
"There is a huge and burgeoning Latino middle class that needs help managing their finances, but advisers need to know how to have the right conversations," Barajas said.
Advisors who work with diverse clients recommend paying close attention to their philosophy on credit card debt, risk versus reward and intergenerational wealth planning.
Respect for elders, for example, is paramount among Asians, which may mean that second- and third-generation clients are unwilling or highly reluctant to address estate planning issues with the family patriarch still living in Tokyo or Hong Kong, Roberts said.
Special tax considerations for foreign-born residents also affect financial planning.
For starters, their investment portfolios are often more complex. That's particularly true among wealthy individuals, who may continue to invest in businesses and stocks in their native country, Roberts said. Others may transfer money to a spouse who is a green card holder rather than a citizen, and a transfer to a noncitizen may be treated as a taxable gift, he said.
Similarly, many immigrants from affluent backgrounds receive money transfers from parents or grandparents back home. Failure to report the receipt of these transfers carries severe penalties by the Internal Revenue Service.
Having a firm grasp on issues such as these will be crucial for advisors who want to build more multicultural practices in the future, experts said.