"Cultural immersion is the most effective way to learn a foreign tongue" because you are forced to communicate exclusively in the foreign tongue. It's a lot more practice in a lot more contexts 100 percent of the time, instead of just some casual class time that you barely pay attention to. It has nothing to do with this fairly irrelevant research about cues for your home culture causing temporary confusion.
Likewise immigrants who settle in ethnic enclaves don't learn the local language as fast for the very simple reason that they don't have to; they get most of their business done in their original language, and most of their social interactions are in their original language. Less practice, less forced use of the new language means slower learning.
I have experienced both alternatives; I have twice been put into complete immersion situations. Both times I learned the local language relatively fluently in about 4 to 6 months. And the one time that I lived in a sort of foreign enclave bubble for two to three years, despite working very hard at studying the local language, I never attained full fluency. It's just too easy to fall back on speaking English if it's there all around you.