So according to EASA, it is the AMCs/GM for Regulation 2015/340, Part ATCO.OR (Annex III to Decision 2015/10/R) and specifically in AMC1.ATCO.OR.C015(b)(b)
where is specifies 11 criteria regarding STD standards, among them being accuracy of aircraft performance, voice recognition realism, equipment, data displays, etc:
STD criteria
If a synthetic training device (STD) is used for training, it should
be approved by the competent authority as part of the course approval process
for any training plan. Training organisations should demonstrate how the STD will provide adequate support for the intended training, in particular, how the STD will meet the stated objectives of the practical training exercises and enable the performance objectives to be assessed to the level determined in the training programme.
This demonstration and the related documentation should include the
following relevant criteria:
(1) the general environment, which should provide an environment in
which STD exercises may be run without undue interference from unrelated activities;
(2) the STD layout;
(3) the equipment provided;
(4) the display presentation, functionality, and updating of operational information;
(5) data displays, including strip displays, where appropriate;
(6) coordination facilities;
(7) aircraft performance characteristics, including the availability of manoeuvres, e.g. holding or instrumental landing system (ILS) operation, required for a particular simulation;
(8) the availability of real-time changes during an exercise;
(9) the processes by which the training organisation can be assured that staff associated with the training conducted with the use of an STD are
competent;
(10) the degree of realism of any voice recognition system associated with
the STD;
(11) where a simulator is an integral part of an operational ATC
system, the processes by which the training organisation is assured that interference between the simulated and operational environments is prevented.
The extent to which the STD achieves the above criteria will be used to determine the adequacy of the STD for the proposed use. As a general principle, the greater the degree of replication of the operational position being represented the greater the use will be possible for any particular training.