Вот нашел более-менее официальное объяснение:
https://shiny.rstudio.com/articles/scoping.htmlThis document describes how scoping works within a single R process.
One R process can support multiple Shiny sessions. Some hosting platforms (including RStudio Connect, Shiny Server Pro, and
shinyapps.io) also allow running multiple R processes to handle heavier traffic.
Within each R process, the scoping works as explained below, but between the R processes, no objects are shared. So, for example, if you configure RStudio Connect to start a new R process for each connection to your app, no objects will ever be shared between different sessions of the app, since these sessions all belong to different R processes
Так что если у вас юзеры не видят реактивные значения друг друга из global.R, то, наверное, они в разных сессиях сидят.