If you're referring to the display, say, on the Navigation Display of a 747-400, the 10 minutes is simply a fixed time period from when the IRS selectors are moved to NAV (or ALIGN). There are no complex nav calculations being carried out in relation to the timer. Indeed, when you are operating from high latitudes, you have to force the IRS's to stay in ALIGN mode for at least 17 minutes (by selecting ALIGN and not NAV until the 17 minutes has elapsed). It would be necessary to measure this time period by something other than the IRS timer.
Re the start of timing period... I have seen operational and training notes to the contrary of what I have said (e.g the timing period begins after the PPOS has been entered), but after many observations of the countdown on the real aircraft, what I have said is true.
Sorry, I don't have any info on why the countown display shows 7+ and not 10.
Regards.
Q.