Drill-down events (like those presented by @edgararuizin this blog post and found in this app work continuously locally but stop after 2 drill-downs once hosted.
In the above app, the tab title displays the correct title but not the correct data (as seen by the dest_name in the drill-down table after selecting the 3rd airport).
The behavior can also be seen be seen in this app. The notification and title show that the correct 'filter' is captured, but the data displayed is not correct after the 2nd tab.
Both apps, so the one under your shinyapps.io account and the one I published. In the one under your account, if you select 3 airports to drill-down, the 3rd tab created will display the data from the 2nd tab.
For example, from the landing page, selecting Hartsfield then Akron Canton then General Mitchell will generate 3 tabs with Hartsfield then Akron Canton then General Mitchell as the tab title. However, the General Mitchell tab will display the same data as the Akron Canton tab.
In the app I published, I followed the code shared in the blog. Clicking a row in the DT table will generate tabs based on the Species selected from the iris data. The 3rd tab generated will display the data for the 2nd Species selected, regardless of the order of selection.