Matomo load-balancing and Tag Manager: missing feature or missing documentation?

As described in the FAQ, I prepared Matomo for load-balancing: 2 “front” machines with tracker and one “UI” machine for the users.
But when the users started to use the tag manager, I figured out that the additional code (in js directory) is generated only on the UI machine, so it was not accessible from the “outside world”.
This means either these files need to become generated on the other machines as well (in that case it’s a missing feature) or the FAQ needs to become extended and state that the “container*js” files need to be synced to the other machines, too (this would be missing documentation).