My first reading of the sentence grouped the words "products they face" together. By the time that I encountered "a trade off" I realized that I had done that in error. A comma after products would have alerted me (and other readers) that there was a separation between "products" and "they face" and we would have avoided that error.
My practice is to read the sentence out loud. If I pause during a sentence, it is typically to signal that the sentence is shifting from one focus to another. I then think of inserting a comma or other punctuation to make my intent, as the writer, clear.
And if we are being fussy, I would also suggest that the "they" in "they face" is a bit ambiguous. One could argue that the pronoun represents the last explicit noun (that makes sense). The noun "products" does not make sense. The noun "consumers" might make sense but it is a stretch. I am pretty sure that you intended "Advertisers" to be faced with a trade off, but that linkage is muddy.
Restructuring the sentence gives me "Advertisers face a trade off when they try to influence the beliefs of consumers about the effects of products." This sentence is not particularly elegant but it unambiguous.