It is largely dependent on the ATSU providers and what they set in each contract. There is all the usual identification of the aircraft and flight Number/Registration/Tail number as well as a time signal when the message (uplink or downlink is sent.
Most have a number of trigger events such as waypoint passage (WCE or Waypoint Crossing Event in ADS speak) and can set values to trigger Altitude excursions and amount of deviation off track. GOLD has a fair amount of detail of the functions that are available in the ADS C systems.
In terms of timing for a data downlink (generally position and currrent flight parameters) the common values as recommended for ATSU providers is not greater than 27 mins between updates in RNP 10 airspace and at intervals not greater than 14 mins in RNP 4 Airspace. It is up to the individual providers to set their own standards, in one of the RNP 4 airspace areas I know that the interval is set at 10 mins.