“Fundamentally, unlike members of the House and the Senate, there’s no element of dependency that goes with being in Washington” for governors, said Mark Sanford, a former governor of South Carolina who recently ended his quixotic bid to challenge Mr. Trump for the Republican nomination.

“There’s a degree of political autonomy” that governors have, he added.

Mike DuHaime, a Republican strategist who advised former Gov. Chris Christie of New Jersey, put it more bluntly: “Many members of Congress are scared of the president’s ability to take them out in a primary — governors are less so.”

The examples have piled up over the last 18 months, as some of Mr. Trump’s aides have winced at how aggressively he wanted to participate in particular campaigns despite their urging him to stay out of those races.

For those candidates who won their governor’s races, their own political needs have since overshadowed those of Mr. Trump, and they have less incentive to fear him once elected.