Tella's brace fired Burnley into the last 16 of the FA Cup on Tuesday to emphasise how important he has become to the club.
He scored after just 46 seconds of Tuesday night's fourth round replay against Ipswich, but Burnley needed his second in stoppage time to see off the Tractor Boys, who had levelled through George Hirst only three minutes into the match, 2-1.
The goals were Tella's 10th and 11th of the season for Burnley, the sort of production goal-shy Southampton might be able to use themselves in their battle against relegation.
"We hid the phones and made sure nobody contacted us," Kompany said with a laugh when asked if Saints boss Nathan Jones had ever asked about recalling Tella. "The last thing we wanted was to ask questions. We're happy he's here with us and that's all that matters."
Tella struggled for playing time with Southampton last season, making only 14 starts in all competitions, and Kompany believes the 23-year-old is thriving on the extra responsibility he has at Turf Moor.
"These kind of players, they need to play, that's the reason ultimately why he's here, but there's never been any doubt about his ability to score and you can see in front of goal, he just needs to get in the right position and he needs to get the service," he said.
"The other side of it is he works hard for the team. He doesn't just strengthen us when we've got the ball. He gives us something when we don't have the ball. It's the right place at the right time for him. After that we'll see but he's doing what he needs to be doing now."
Victory gives Burnley a last 16 tie at home to League One Fleetwood, offering a clear opportunity to reach the quarter-finals for the first time since 2003.
Kompany's priority remains the league - as shown by the seven changes he made to his line-up - but there would be no harm in a Cup run.
"We've given everybody a little bit of hope," Kompany said. "That's good. It's something that's going to live in the background, but we can go back to trying to be a good team in the Championship and that will be our main focus now."
Having held Burnley to a goalless draw at Portman Road, Ipswich again showed why they are in the thick of the League One promotion race with a battling performance.
Although Tella's late strike came as a cruel blow, Ipswich boss Kieran McKenna made the long journey home a happy man.
"I'm really proud of the players and proud of the supporters," he said. "I thought it was a very good performance against an outstanding side.
"We went toe-to-toe with them, we played bravely without the ball and we represented ourselves how we wanted to, especially after conceding so early. We just got caught out by the speed and the quality of an opponent we don't face very often.
"To show the response that we did, the players can take great pride in that. The key bit now is how we can use the lessons and the level of the opponent and the level we showed across the two games to give us a boost and help us for the rest of the season."