Your Oceanic cleared route is thus:
ATSIX 62N020W 63N030W 63N040W 62N050W 59N060W LAKES
You've already got this route loaded into the FMC, as you were fortunate enough to get your flight planned route, and within that route stored in the FMC is a crew swap reminder at 6107N01500W.
You've set up the ADS-C Waypoint Event Contract which will downlink, via satellite, all waypoint position reports during the crossing and, additionally, you've logged on to EGGX for CPDLC.
As you progress ATSIX, ADS will downlink to ATC:
ATSIX/1305 33O 6107N01500W/1318 NEXT 62N020W
(Waypoint/ATA, Level, Ensuing waypoint/ETA, Next ensuing waypoint - identical to the HF voice format)
Because the above ADS waypoint position report does not exactly correspond to those significant waypoints in your cleared route, ATC must ask you to confirm the ETA for 20W and the co-ords of the "NEXT" waypoint (30W) reflected in the clearance. An HF message may be sent by ATC asking you to do this, or a CPDLC format message may be uplinked by ATC, e.g:
[CONFIRM ENSUING WAYPOINT]
[CONFIRM NEXT WAYPOINT ETA]
[CONFIRM NEXT ENSUING WAYPOINT]
The format of the ADS report which ATC would expect to see, corresponding exactly to the cleared route, would have been:
ATSIX/1305 330 62N020W/1338 NEXT 63N030W
Should anything other than the above be downlinked, ATC will query those elements which do not correspond to the cleared route/level/credible ATA/ETA.
This situation applies to all waypoints on the route stored in the FMC to highlight FIR boundaries, crew rest/swaps, turnback/diversion points, etc. which are in addition to those significant waypoints specified in the oceanic clearance.
For info, we see everything you do in terms of adjusting the route once within oceanic airspace, be it to set up SLOP, deviate due weather, strip out some points to calcualte an arrival time at destination, etc., and it is easier for us to detect who is not following the route specified in the clearance.
Hope the above helps.
Having just looked at your initial question again, as far as the crew are concerned, ADS will downlink only when the aircraft crosses a waypoint on the route stored in the FMC or when the crew alter the route held in the FMC (once the aircraft is within oceanic airspace, e.g. for WX deviation).
However, ATC can at any time select a "Demand Contract" - which will downlink to ATC the aircraft's present position plus the ensuing waypoints.
Other ADS contracts can be set up, such as the "MET contract", which sends a report every 30 minutes, or the "R-LONGSM (Reduced longitudinal separation minima) Contract", which reports every 18 minutes, but these are as invisible to the crew as they are to ATC. (ATC can only see such reports in the flight's "History" and in any event they would be of limited use).
The data from ADS/FMC and HF reports are used at Shanwick to provide a picture on a 'pseudo radar' display (Graphic Data Display) showing the approximate position of aircraft. It is not (yet) used as a tool for separation purposes but simply to give the controller a real-time 'picture' of what is going on where and in relation to whom. (The system will 'plot' the aircraft position between waypoints on the basis of stored Met and aircraft speed, hence the aircraft symbols will move across the screen as the associated aircraft transit oceanic airspace, thereby making the display 'look' as though it were radar).
A couple of pix online of our own kit (top) and the Canadian kit upon which it is based.(bottom)
(bigger version here