I don't know that you have to have physical evidence or proof of your people-to-people contacts. I don't believe there are any specific articulated requirements for showing Proof."
Number 13 of the Treasure Dept. FAQ (updated October 2016) provides guidance on what constitutes "people to people travel":
https://www.treasury.gov/resource-center/sanctions/Programs/Documents/cuba_faqs_new.pdf
There does not seem to be any requirement for "proof." As I interpret the rules (which seem to change frequently), it's basically on the honor system. You can choose to either obey the law or flout the law. To comply, Number 13 of the FAQ indicates the traveler must "maintain a full-time schedule of educational exchange activities intended to enhance contact with the Cuban people, support civil society in Cuba, or promote the Cuban people’s independence from Cuban authorities, and that will result in meaningful interaction between the traveler and individuals in Cuba." "Tourism" is still expressly prohibited. I suspect a lot of Americans traveling to Cuba at present are simply flouting the law because they believe there are no longer any legal consequences.
Just my interpretation of the present situation and my speculation about what some of my fellow Americans are doing. I'm not advocating for or against anything.