Border guards are allowed to ask you questions to see how you react and to corroborate your story.
If someone (from any country) entered claiming to be a physicist, would it be reasonable to ask him to try to solve some integrals?
How are immigration officers supposed to do their jobs? The purpose of immigration officers isn't to just blindly stamp passports; they actually have to determine if the person attempting to enter should be allowed to enter. Which interestingly, is the job of immigration officers across the world.
I feel like people are just looking for fight and begging for something about which to be outraged. Immigration and Customs officers from all countries have been doing this as long as there have been Customs and Immigration.
(Not saying that this is the correct approach, just saying that this is possible if correctness is not a goal.)
Whether this relates to Trump: As others have pointed out, yes this has been happening before Trump, I'm not alluding to Trump being the sole cause. The point that I'm making is that leaders (president and even local leaders) who can make statements or take actions that are contrary to the country's laws have an effect on the guy on the streets. If you tell me that foreigners are taking our jobs (regardless of its truth), I might not be very objective as a CBP employee. I might even be biased against certain people, but that's hard to judge as we are different as humans.
The guy on the tweet said he was asked 10 other questions, and they seemed to expect textbook/Wikipedia type answers. A blog post from him will hopefully have more details for us to make better observations. You make a fair point about the physicist, but everything in moderation is fair.
My point if any, is that what leaders/politicians say affects our attitude and often opinions. Whether we like such leader or not, I hope we can agree on that at least.