The Trust, which owns City, approved a motion in October to ask the club's board if Tisdale had a notice period and, if so, serve him that notice.
Tisdale had a two-year rolling contract and is now serving that notice period.
It means that unless a new deal can be reached, Tisdale, who is the longest-serving manager in the EFL, will leave Exeter City in November 2018.
Exeter City say they will not comment on the contractual status of any of their employees, while the Trust chairman Martin Weiler told BBC Sport that "the club are aware of the Trust resolution."
Tisdale is not under any immediate threat of the sack, with the Supporters' Trust saying last month that "members wanted to be satisfied that there was a contract that protected the best interests of the club, the trust and the manager."
Exeter are 23rd in League Two, having not won a game at home since April.
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It prompted the Trust to issue a statement on the club's form, which read: "Trustees considered letters from a number of members expressing dissatisfaction with current results.
"The Trust Board shares these concerns and stressed the need for improvement to club board chairman Julian Tagg."
Tisdale. 43, has been in charge at Exeter City since 2006.
He led the club to promotion from the Conference to League Two in 2008 and onto League One the following season, but they dropped back down to the fourth tier in 2012.
Exeter have been owned by their supporters since 2003, when a group of fans bought the club after it had amassed debts of more than £2m after relegation from the Football League.
The Trust has overall control of the club, with a board of directors running Exeter City on a day-to-day basis and a number of Trust members sitting on the club's board.
Exeter City's Supporters' Trust has ordered the club to serve notice on the contract of manager Paul Tisdale.