Roughly, 1990.

A clear gradient of smoking prevalence across income strata was also found. When reviewing studies by decade, only those performed since 1990 showed a strong association.

-- From Association Between Cigarette Smoking Prevalence and Income Level: A Systematic Review and Meta-Analysis

It should first be noted that this isn't just a US effect -- this is an international one. However, since the question was focused on the US, I'll discuss that in particular.

Anti-tobacco campaigns can be dated back to the 19th century, but there wasn't really a notable impact on consumption -- it increased all the way up through WWII. While there was studies linking lung cancer to smoking as early as the 40s, and laws prohibiting cigarette sale to minors were around by the 50s, it wasn't until the 60s that any concerted effort to turn the prevalence of smoking around started; notably, Kennedy commissioned a study that became the 1964 report Smoking and Health: Report of the Advisory Committee to the Surgeon General of the Public Health, 1966 was the first appearance of "cigarette smoking may be hazardous to your health" warnings, and anti-tobacco advertising started in 1967, with $75 million worth of airtime (all free) between 1967 and 1970. A ban on radio and television advertising of cigarettes was the brainchild of the cigarette companies themselves, essentially unilaterally stopping both streams. Cigarette company expenditure on marketing then dropped significantly before slowly revving up again; at the same time, this caused the packs-per-capita level (which had been dropping with the advertising) to return in 1971 to the 1965 level.

However, the slight rise in tobacco use was short lived, and there was a fairly continuous drop starting not long after Anti-tobacco forces kept building up steam, especially with the addition of second-hand smoke research tossed into the mix.

However, what question concerns is not the reduction of tobacco use in general but the split between income demographics. Any explanation will have to adequately account for a.) the fact the phenomenon is not US-only and b.) the enormous amount of reduction that happened without the split.

This is a contentious enough topic that I can't give any answer with certainty, but my best assessment of the sources -- and something that accounts for a and b both to an extent -- is that tobacco companies shifted from advertising to more direct marketing strategies. That is, ad spend in 1970 was 82% of the marketing budget of tobacco companies, and it had dropped to 17% by 1991. As tobacco companies are themselves international any strategies they adopt can affect the market holistically.

By 1991, the largest expenditure became promotional items and discounts. Things like T-shirts and other merchandising make consumers themselves into the ads, and are much more targeted at particular demographics; people who are price conscious (that is, lower income) are more likely to care about the presence of discount coupon campaigns. So while there were still new ad approaches (perhaps most infamously for the time, Joe Camel, originally from a French campaign in the 70s, adapted for the US in 1988) these were meant as a way to continue the same strategy; having "cool" logos that could appear on worn merchandise that did not have to carry any kind of warning label.

To summarize:

a.) the tobacco companies shifted strategy from general advertising into more direct marketing

b.) the nature of the direct marketing was more likely to appeal to lower-income consumers

c.) the logo-merchandising strategy also encouraged a networking effect, again more likely to affect the lower-income consumers

...

Bonnie, R. J., & Lynch, B. S. (Eds.). (1994). Growing up Tobacco Free: Preventing Nicotine Addiction in Children and Youths. Washington, D.C.: National Academies Press.

Casetta, B., Videla, A. J., Bardach, A., Morello, P., Soto, N., Lee, K., Camacho, P. A., Hermoza Moquillaza, R. V. & Ciapponi, A. (2017). Association between cigarette smoking prevalence and income level: a systematic review and meta-analysis. Nicotine & Tobacco Research, 19(12), 1401-1407.

Ibrahim, J. K., & Glantz, S. A. (2007). The rise and fall of tobacco control media campaigns, 1967–2006. American Journal of Public Health, 97(8), 1383-1396.

US Department of Health and Human Services. (2000). A historical review of efforts to reduce smoking in the United States. Reducing Tobacco Use: A Report of the Surgeon General. Atlanta, Georgia: U.S. Department of Health and Human Services, Centers for Disease Control and Prevention, National Center for Chronic Disease Prevention and Health Promotion, Office on Smoking and Health.