The Tech's do all of ours (all our HD & HDF machines have one / two): The staff (and home patients) are under instruction to make contact with us when the 10 remaining treatment warning comes on and we deal with it next time we visit that site. We often do a sweep of the machines so we can guess what to expect in the coming weeks and plan our movements accordingly.
We do a Tiutol clean prior to filter replacement (a hot citric cycle at all other times) and historically it was felt better left to the techs to manage the use of this solution so it isn't left lying around. Also as it's arguably a maintenance task, when we do it the machine's history will contain a record to prove timely exchange of the filters.
On the V9 machines a (longstanding ) software issue means the only way to select the Tiutol clean option is to go in and out of TSM -something we don't want the nursing staff poking around in.
We use the enter key under the screen (many units don't) to confirm data entry. If that option is set the disinfectant choice in the disinfect screen doesn't stick (on V9 software, it works as advertised on V8). We have to go into TSM, change 'enter key confirmation' to 'screen confirmation' to make the Tiutol choice stick, do the filter replacement, then go back into TSM and re-enable 'enter key confirmation'. All a bit tiresome...
The Tiutol clean is damaging to the filter itself, so can only run just prior to replacement, but we're told it strips any protein / fat / gunk from the machine that citric alone may not tackle. We've always run that way so I can't say if never doing a Tiutol clean leads to anything building up in the machine.