OK, I think I see what's happening here with the HQ liberations.
The mission to hijack the ship is highly random. There's not necessarily a time limit at all, or there could be a relatively short time limit. From the ones I've seen, when there's a time limit it's until the ship gets to the HQ. So in those cases, the longer the timer runs down, the less time you have at the end to escape.
If you set off an alarm, the ship also starts heading right for the HQ, and on non-timed missions it seems to just kinda hang out nearby, so you don't get much time here either.
Finally, when you do hijack the ship, you send it on a crash course into that HQ. So the ship's destination is that HQ in almost all cases.
As for the 1 second timer upon hijacking, that seems to be a display bug.
I was on a hijack mission with no mission timer. The ship seemed to be flying a lazy circle a ways from the HQ. In the process of hijacking, I caused an alarm, which gave me about 40 seconds. I made it to the captain's seat with about 24 seconds remaining on the timer. Before hijacking and setting the course, I paused and zoomed out. I was a good way away from the HQ, 24 seconds seemed pretty reasonable.
I then hijacked the ship, set the course, then immediately paused and zoomed out. I was at the same distance as before, only now the timer said 1 second. I unpaused for a moment to observe the ship speed while zoomed out, it wasn't moving ultra fast or anything. There was no way I was going to hit the station in 1 second at the speed I was going, the 24 seconds from the alarm seemed closer to correct.
So I unpaused, and ran like hell to the nearest window (not that near either). The timer counted down from 1 to 0 in about... 3 seconds? I paused and zoomed out again, still quite a ways from the HQ, even though the timer says 0. I continued running, for a lot more than 0 seconds, and jumped out the window. The ship was about halfway to the station by now. I caught myself with my pod, flew toward the station, when finally the ship hit, mission complete.
So what I think is happening here is that the dev has made a very simple math error. I believe normally the timer displays work like this:
(Timer_Display = Elapsed_Mission_Time - Total_Mission_Time). Where total mission time is either the mission timer or the alarm timer. This would mean the timer display is really a negative number, which seems odd, but it's the only way I can make sense of the HQ timer bug.
I think in the case of HQ missions, he somehow divided instead of subtracting. This formula gives the same results, although it's different enough from the correct formula that I'm probably getting this slightly wrong.
That equation would be (Timer_Display = 1-(Elapsed_Mission_Time / Total_Mission_Time))
That equation would start giving a result of 1, (0/anything = 0, 1-0 = 1.) As the elapsed time counts up, your result keeps going down.
(10/100 = 0.1, 1-0.1 = 0.9)
The other piece of the puzzle is that the timer display has no decimal places. And I would guess that it's stored as an integer rather than a real number. That would mean the result probably gets rounded or truncated, and since the timer seems to show 0 a lot longer than it shows 1, my guess is that it is truncating. If it were rounding I'd expect the 1 to last just as long as the 0.
I'm probably somewhat wrong on the specifics, but I think that's the general idea of what's going on there.