President Trump was peeved.

Just minutes before he walked into the Oval Office for a televised send-off for Elon Musk, an aide had handed him a file.

The papers in that file showed that Mr. Trump’s nominee to run NASA — a close associate of Mr. Musk’s — had donated to prominent Democrats in recent years, including some who Mr. Trump was learning about for the first time.

The president set his outrage aside and mustered through the public farewell, with both men praising each other and saying their relationship would continue. But as soon as the cameras left the Oval Office, the president confronted Mr. Musk.

Mr. Trump started to read some of the donations out loud, shaking his head and pointing out several of the most recent ones in the file. This was not good, the president said — an early signal of the simmering tensions between the two men that would explode into the open less than a week later.

Mr. Musk, who was sporting a black eye, which he blamed on a tussle with his young son, tried to explain. He said his friend Jared Isaacman, a billionaire entrepreneur who was set to become the next NASA administrator, cared about getting things done. Yes, he had donated to Democrats, but so had a lot of people.

Maybe it’s a good thing, Mr. Musk told the president — it shows that you’re willing to hire people of all stripes.