The counterfactual model for causation My professional training took place in the late 1990's and I don't recall hearing some of the terminology that seems nigh-universal nowadays. I believe the accepted name is "counterfactual model for causation", often used by Sander Greenland and other widely-respected Epidemiology authorities. I have a couple of questions:
Is that line of reasoning and set of terminology considered mainstream and uncontroversial? Versus there being competing frameworks of which the "counterfactual" thing is merely in contention for acceptance.
And what was the general timeline for adoption of that way of viewing things like confounding, estimating intervention effects and so forth? 
 A: I wouldn't say it is uncontroversial because the answer to the question "what does it mean for A to be a cause of B?" can be answered in different ways within philosophy. 
The best know counterfactual theory of causation  is David Lewis's (1973b) theory. David Lewis also did important work on possible world semantics which he used to analyze causal statements. 
The basic idea is that causal statements are equivalent or at least imply counterfactual statements. 
So the statement "A causes B" imply that 
(1) "If A had happened then B would have happened" and
(2) "Had A not happened then B would not have happened" 
These sentences can then be analyzed in possible world semantics for an easy read see link.
One can offcourse accept such implications of causal statements without buying into David Lewis' theory. So given that causal statements imply counterfactuals how has this been applied in social science? Well:
From a social science perspective using quatitative statistical methods two authors should be mentioned: 
(1) The Rubin causal model (RCM), also known as the Neyman–Rubin causal model RCM. Which has been put to use in the estimation of treatment effects. 
Here the basic idea is that for each observational unit both a state $Y_0$ without treatment is hypothesized as well as a state $Y_1$ with treatment. The observed effect is $Y$ which is defined as
$Y = Y_0 (1-I) + Y_1 I$
where $I$ is indicator of treatment. Hence only one of the states is observed or realized depending on whether the observational unit is treated or not. To put it in terms of possible world semantics only one of the states is actual whereas the other is counter factual. The causal effect is the difference between what happened and what would have happened: $Y_1 - Y_0$, had treatment not been given. 
The Rubin causal model was pioneered in 1974 and has made its way in standard reference works in for example econometrics such as Jeffrey M. Wooldridge (2002 1ed)(2009 2ed) "Econometric Analysis of Cross Section and Panel Data". Hence anyone who claim to have training in advanced econometrics now adays would most likely know RCM.   
Another important author is 
(2) Judea Pearl a computer scientist and philosopher, best known for championing the probabilistic approach to artificial intelligence and the development of Bayesian networks see wiki reference. 
His approach to causation while still counterfactual is more informed by the concept of a directed graph. To mention some of his works the long but good version is "Causality. Models Reasoning and Inference" (2000 1ed)(2009 2ed), a primer "Causal Inference in statistics" (2016) or for an article summarizing the main ideas see "Causal inference in statistics: An overview" Judea Pearl (2009) Statistics Surveys Vol. 3 pp. 96-146.
Some of his main ideas are introduced in such standard texts on machine learning as "Probabilistic Graphical Models. Principles and Techniques" (2009) by Daphne Koller and Nir Freidman (see chapter 3).
So to the extent that the ideas of these two seminal authors have made their way into standard reference texts "the counterfactual model for causation" is uncontroversial. 
For an excellent introduction to these ideas and a nice overview of the origins of this litterature see the book
"Counterfactual and Causal Inference. Methods and Principles for Social Research"(2015 2ed) Stephen L. Morgan and Christopher Winship. 
I would say this book is on textbook level so that says something about how common the ideas and analytical techniques have become. Also this book tries to integrate or at least present together the ideas that have been developing since the 70's.
A: 
Is that line of reasoning and set of terminology considered mainstream
  and uncontroversial? Versus there being competing frameworks of which
  the "counterfactual" thing is merely in contention for acceptance.

Likely depends on who you ask. But for an epidemiologist at this point? Pretty much yeah. It's also an immensely useful framework for thinking about studies and questions in epidemiology.

And what was the general timeline for adoption of that way of viewing
  things like confounding, estimating intervention effects and so forth?

At the very least, it appears in Modern Epidemiology 3rd Edition by Rothman, Greenland and Lash, one of the cornerstone textbooks of academic epidemiology, and that was published in 2008. It was about that time I started graduate school in epidemiology, and it was the standard way we were taught. That might have been a bit early, as I was at a somewhat methods heavy institution, but it's a reasonable estimate for "This is now the mundane and accepted approach to this".
