Wikipedia describes the way the US ambassador and other members of the diplomatic corps were treated. Ultimately they were exchanged for German prisoners. Is that usual to exchange diplomats for other prisoners? Why were they not immediately sent to a neutral country or put on a neutral ship? I understand that after Pearl Harbor Japanese diplomats were sent home.
Sounds to me they were kept in a secure location until they could be repatriated (remember there were no ways to do so using normal means at the time as there was no shipping between the countries while they were at war).
As the USA also held German nationals in similar conditions, it was a natural that they would be handed over at the same time, both groups in effect serving as hostages for the well being of the other.
While they reported of a lack of food, that was probably no worse than not having their normal excess they were used to in pre-war Berlin. The entire German population was on rationing, it would be quite normal that the US diplomatic group was similarly limited in what they had available to them (in fact the same was true of POW camps, while indeed conditions there were harsh and food scarce, it was not much more so than for the population in the surrounding towns and German authorities (probably correctly) assumed that if they supplied enemy prisoners with more food than the local population they'd have riots on their hand).