He netted twice for Championship leaders Burnley, along with a double from Manuel Benson, to give the Clarets their 14th victory in their last 17 fixtures and earn a place in the fourth-round draw on Sunday.
“It felt like it announced his comeback from the World Cup,” said Clarets boss Kompany.
“He hadn’t done anything wrong since arriving back but you could see he was catching up physically.
“The technical ability he showed in tight spaces isn’t easy to teach.
“We started the beginning of the season with a kid who needed to prove he could play in English football, and fast forward six months and we have a superstar.
“He has come back from playing in front of millions of people on the Moroccan streets. He didn’t just make us proud but the whole of Africa.
“He has to get through the change of lifestyle but he is in a good place and today he showed he is just cracking on with his work and not changing anything.
“He still has as much to improve on as a couple of months ago.”
Three of Burnley’s goals came about following blunders from Bournemouth players.
They took the lead when Marco Senesi’s loose pass was picked off by Johann Berg Gudmundsson, who threaded Benson in behind for his eighth goal of the season.
However, the Cherries were level after 12thanks to another error, when Burnley midfielder Josh Cullen sliced a first-time pass on the edge of his own area to give Ryan Christie an open goal.
Tardy Lewis Cook was hounded off the ball by Ashley Barnes in the 39th minute before Josh Brownhill gave Zaroury a tap in before the Moroccan skipped through the defence for a wonderful second to make it 3-1 at the interval.
Christie’s slack header then gifted a fourth for the visitors, with Benson converting again, before Dominic Solanke’s consolation.
Bournemouth boss Gary O’Neil was not impressed by the individual mishaps.
“The three huge errors for the goals make it impossible to win the football match,” he said. “That is the story of the game. We stood no chance.
“There is a clear understanding of where we are and where we need to get to.
“It is five losses on the trot but three of them are away to Newcastle, Chelsea and Manchester United, but there are two in there where we could do something about it – we beat ourselves in both of them.
“I’m working hard with the players but it becomes harder when you aren’t winning.
“There is a process to fix them but there is no magic wand.”