OK, some intervalometer testing on a D810.
I have the intervalometer to take 3 photos. I'm in manual exposure mode, manual focus, with the lens cap on to simulate dark skies. Long exposure NR is off. High ISO NR is set to 'Normal', which is the default (and what the OP used), but ISO is only 500 (also what the OP used) so I wouldn't expect that to be an issue.
Exposure time = 5s, interval time = 6 s.
5s exposure, 1s gap, 5s exposure, 1s gap, 5s exposure. As expected.
Exposure time = 10 seconds, interval time = 11 seconds.
10s exposure, 1s gap, 10s exposure, 1s gap, 10s exposure. As expected.
Exposure time = 13 seconds, interval time = 14 seconds.
13s exposure, 1s gap, 13s exposure, 1s gap, 13s exposure. As expected.
Exposure time = 15 seconds, interval time = 16 seconds.
15s exposure, 17s gap, 15s exposure. No third exposure.
This sequence of results is completely repeatable.
Exposure time = 15 seconds, interval time = 17 seconds.
15s exposure, 2s gap, 15s exposure, 2s gap, 15s exposure. As expected.
Exposure time = 20 seconds, interval time = 21 seconds.
20s exposure, 1s gap, 20s exposure, 1s gap, 20s exposure. As expected.
Exposure time = 25 seconds, interval time = 26 seconds.
25s exposure, 1s gap, 25s exposure, 1s gap, 25s exposure. As expected.
Exposure time = 30 seconds, interval time = 31 seconds.
30s exposure, 32s gap, 30s exposure. No third exposure.
This sequence of results is completely repeatable.
Exposure time = 30 seconds, interval time = 32 seconds.
30s exposure, 34s gap, 30s exposure. No third exposure.
This sequence of results is completely repeatable.
Exposure time = 30 seconds, interval time = 33 seconds.
30s exposure, 3s gap, 30s exposure, 3s gap, 30s exposure. As expected.
Well, I say this last one was "as expected". The EXIF data says the exposure time was 30s and the time interval between consecutive exposures was 33s, but the gap didn't sound like it lasted 3s. So I timed it by hand. I measured the exposure at 32s and the gap at 1s. Then I went back to the 15s exposure and timed it by hand. Guess what? It was 16s.
So then I went back and manually timed all the exposure settings from 5s upwards. Here's what I got.
Indicated exposure: 5, 6, 8, 10, 13, 15, 20, 25, 30.
Measured exposure: 5, 6, 8, 10, 13, 16, 20, 25, 32.
I think that explains my results perfectly, and it also explains the OP's problem, and it explains why the internet sources the OP mentioned recommended setting the intervalometer to 33 seconds.
It would be interesting to know whether this discrepancy between the indicated exposure and the actual exposure is specific to the D810, or whether all Nikons do it, or whether all cameras do it. It obviously arises as a consequence of needing to double the exposure times (1, 2, 4, 8, 16, 32) in order to maintain exact 1-stop gaps between them, so it wouldn't surprise me if it turned out to be quite widespread.