Jersey head coach Harvey Biljon has urged the club and supporters not to get "carried away" as they moved to within two points of the Championship play-off zone.
The islanders climbed into the top half with a 35-7 win over struggling Ealing Trailfinders on Friday.
It is the first time Jersey have won three consecutive league matches since promotion to the Championship in 2012.
"Let's keep our feet firmly on the ground," Biljon told BBC Radio Jersey.
"We've got to stay on task and make sure we keep our focus. We need to make sure we continue to build on these performances."
Away wins over London Scottish and Rotherham Titans, followed by the home victory against bottom club Ealing, have helped the islanders to sixth place at the midway point in the season.
"I'm just really proud that the players could put on a performance in front of the home supporters," added Biljon.
"We've done it against London Scottish, we did it against Rotherham and all week we spoke about making sure we could put on that show.
"It's the first time Jersey have won three games on the bounce in the Championship and that's pretty important."