A union said the faces idea at a Revenue and Customs office in Swansea was part of a scheme being tested by the department after it hired outside consultants.
The Public and Commercial Services union also claimed workers had to predict the exact time they would arrive in the office, have a lunch break, and leave for home to allow for "accurate targeting of work".
A growing number of meetings were also being held, including some on how to sort out the "problem" of establishing when workers were at lunch.
PCS leader Mark Serwotka said: "This is yet another crazy example of a scheme dreamt up by consultants earning huge amounts of taxpayer's money — at least £1,000 a day.
"Not only is it demeaning and demoralising for skilled staff, but comes at a time when Revenue and Customs are ploughing ahead in closing offices and cutting jobs.
"These aren't primary school children working in this tax office, but experienced staff who collect the taxes that pay for our schools, hospitals and other public services.
"To add insult to injury they also face the possibility of some of their tax collection work being privatised. The department need to intervene and drop this scheme and ditch its plans to cut jobs and close offices."