And how do you disembark from a ship in a foreign country without a passport?
That answer is that, in very many countries, the cruise line submits passport information en bloc to immigration authorities in advance of arrival. In others immigration board the ship on arrival, and do an overall check with the ship's purser before the ship is cleared for passengers to disembark. Just one of the many checks which is made on a ship when it arrives in any port and one of the reasons why the ship doesn't just moor up and then you have to wait a while to disembark.
It would be quite unusual in my experience, at a port call, to go through actual formal immigration standing in line at a desk in the way you do if you fly in.
New information is that the ship had waited for over an hour already for these passengers. In that time their passports had been obtained (either from the cabin or the purser's office) and transferred ashore. Also NCL are only covering their travel costs from the cancelled port call in Gambia to Senegal, not the initial sector from Sao Tome to Gambia.
I have enough experience of tendering to know that if a ship arrives at 7am, then tendering ashore is unlikely to start significantly before 8am.
Tenders have to be lowered, then shore crew taken over, the tender dock prepared etc- it all takes time.
Usually early tenders are for ship's excursion passengers only. So, as an independent passenger, I would not budget to be stepping ashore at a tender dock much before 10am. Earlier would be a bonus. Often too tender tickets are allocated on a first come first served basis the previous day.
In this case all aboard was at 3pm- so last tenders probably 2.30pm. I would want to be back at the dock a good half hour before that. Thus I would not have expected to have more than 3 to at very best 4 hours ashore. I would tailor my expectations of my shore time accordingly.
And I have never been on a cruise ship (or indeed freighter) where the daily programme does not have a ship's 'phone number on it. On most ships I have been on you are also given the Port Agent's number. I treat this claim of having to e-mail or call the contact centre in the US as total baloney. Sao Tome was not the first port call on this voyage, so even if the programme on NCL is now virtual (not printed) and they had not downloaded that day's schedule a previous day would have had the ship's number on.