To be clear, specifically, I'm wondering if the persons present for the reading of the verdict in "Bridge of Spies" were applauding because they personally were pleased with the result or if they were applauding because there would be repercussions from the government (of any level) if they did not.
For reference, here's British Pathe's contemporary coverage of the trial. For folks who want/need a YouTube link, this silent film includes footage starting about 1:10. Before that, are Soviet displays of the U-2 wreckage.
As to the trial, we should establish that the applause was not just a Hollywood invention. This was a show trial, and the world press was invited. As Life Magazine recounted in its Aug. 29, 1960 issue:
"'Because of his sincere repentence,' Rudenko went on, 'I shall not ask for the supreme punishment. I ask 15 years of dentention.'
There was a little cry from the box. Barbara Powers and Jessica Hileman collapsed with their heads in their laps, weeping. Oliver Powers tried unsuccessfully to wave away a Soviet movie cameraman. He then rose and standing, with his hands by his sides, he looked down at his wife. The sound of clapping hands filled the room as most of the audience stood up to applaud.
'Give me 15 years here,' Oliver Powers cried to one of the American lawyers with him, 'I'd rather get death.'"
The Powers trial was a show trial designed for maximum exposure. It was intended to showcase not only America's error but also the "humaneness" of the Soviet system, which sentenced Powers to 10 years imprisonment. Even the audience was carefully selected, with military and government officials filling the spectators' chairs. Powers' family was present, as were members of the media and American ambassadorial staff, so the applause would not have been universal.