The Dutch defender spent three years with the Bhoys before moving to Southampton during the summer transfer window.
“I think he found it too easy in Scotland,” Thompson said.
“I see him on the left of the penalty box, and on the right doing things. And you think ‘what is he doing here?’
“But he has so much confidence in his ability. I think he’s been a fantastic signing.”
Van Dijk has slotted straight into Southampton’s team, and his performances alongside Jose Fonte have been highly impressive.
While the 24-year-old has helped to tighten up the Saints’ defence, he has also added a greater attacking threat due to his ability from set-pieces.
Ronald Koeman’s side have already benefited from Van Dijk’s arrival, and there is an expectation that his performances will become even stronger as the season progresses.
Southampton are currently sat in eighth place in the Premier League table, with their next match coming against Manchester City at the weekend.