They are basically just for doing data wrangling and cleaning with time series, you would need a separate package to fetch the remote data, if the source is a database dbplyr would play nice with tsibble since they are both part of the tidyverse, if the source is an API then take a look to httr package.
Also, I think that for easing real time data acquisition and to make it more similar to your phone app, you would have to develop a shiny app.