This is a very difficult question to answer because of at least three factors:

a) Productivity growth as a discipline did not really take off until the 1960s with the release of the Solow model
b) Economists argue about what "productivity" is on a daily basis. An observed collapse in productivity from the 1980s to the present is one of the defining breaks in the literature. Some economists argue that this is due to changing macroeconomic conditions, such argue that it is correlated to depressed wages (as in a perfect world market wages are theoretically equal to the marginal product of labor), and some argue that we just aren't capturing productivity properly. This was true for instance of the first computers in the 1990s when Solow remarked that "you can see (computers) everywhere except for the productivity statistics." We see computers and computerized devices even more now. Are we capturing them properly?
c) Television may have distracted people from work, but it also provided them with information-as well as advertising through which it improved "marketing" productivity. Why post posters advertising your business when you could run a TV ad instead? Arguably cell phones are just an extension of this.

I notice in the report that the argument is made that the drop in productivity is coincidental with the rise of smartphones. I offer the much more rigorous explanation that is offered by BLS here as an alternative: namely that the denominator of labor productivity, hours, has been growing roughly at the same rate as production, since the 2008 recession. This would logically result in lower labor productivity. In essence people need to work more to make enough money to buy the goods they need. Now whether they are being less productive during those hours is another issue, but suffice to say that there are many things that can distract people in the work place aside from just cell phones. In Japan, for example, many people spend their long hours idling or reading newspapers.