The word all you non-lawyers are looking for is the legal term"exclusion". That occurs usually at the airport when arriving and going through immigration. Or when crossing the border in Mexico and Canada. It is different from deportation. People first arriving may be excluded for almost any reason that is not deemed arbitrary or capricious. ICE is historically given tremendous latitude to exclude people. Usually people excluded include those who appearto have arrived in the USA to seek employment when all they have is a tourist or a student visa. One of the primary ways they verify that a foreigner truly is just a tourist is to verify their financial status in their home country. People who are young, don't have much money, or a set tourist itinerary are often suspected of really coming here just to work. They get excluded by immigration all the time.

Read this. Understand this. And you will have learned something all Americans should understand. It will also add a lot more clarity to what you all are attempting to to discuss. These tourists' sound like they were excluded, not deported. Legally a very substantive difference.