The tidyverse is a set of packages designed for interactive data analysis. r-lib packages are more developer-oriented utilities.
The r-lib organisation (in GitHub parlance, it is an organisation) is a collection of fundamental infrastructure packages like R6, xml2, fs, and testthat. The packages that are part of that organization are ones we see it as a piece of important infrastructure for the R community.
The team I work on at RStudio is something to the effect of the tidyverse/r-lib team. That is not to say that all of the creators/authors/maintainers of the packages work at RStudio (they don't). This is especially true of r-lib. (You can peruse the GitHub organization, members, and packages, which will show this better than I could describe.)
If you're asking about the use of NSE in the tidyverse, then yes. The links at the bottom of the vignette you linked to above go to the first edition of Advanced R. The second edition uses rlang and tidy eval.
tidyverse packages either have or are moving to support tidy eval, e.g. ggplot2 now supports tidy evaluation, as part of our making this consistent throughout the tidyverse