1. He was talking to people at the coffee shop.

[Does 'at the coffee shop' modify 'people' or 'talking'? Is it an adverbial phrase or an adjective phrase?]

2. He was talking to 'the people' at the coffee shop.
[Does 'at the coffee shop' modify 'the people' or 'talking'? Is it an adverbial phrase or an adjective phrase?]

1. and 2. -- Since "at the coffee shop" occurs right after "people," it's an adjective phrase, modifying "people."

English depends a great deal on word order in sentences. Other languages (such as Latin, French, and many others) depend on specific endings on words to tell which modifies what.