Palace were comfortable 2-0 winners over Cardiff on Saturday as Pulis notched his second win in three matches since taking up the role a little over a fortnight ago.
And Jerome believes that Pulis is already proving to be the right man to take the club forward.
"From a personal point of view and the team's point of view, it's magnificent that someone like that has come in," Jerome said.
"Since he's come in he has carried on the momentum that [caretaker manager] Keith Millen built up over those three or four games.
"Tony has come in and he has had a big impact. The boys have responded well to him and we're getting good results now."
Jerome, on a season-long loan deal from Stoke, was on the scoresheet for the first time since February in Saturday's victory over Cardiff.
The 27-year-old revealed Pulis' appointment has had a positive effect on his own confidence, but insisted the most important thing was for the team to continue to get positive results.
"Coming in here, playing games and getting a run in the side for the last three or four games and obviously getting the goal - the confidence is there," Jerome said.
"It's been a while since I have been playing games. Now I have come in and played a few games and gone on a run.
"The results are starting to come for the team too and that's the most important thing. We talked about setting the tempo early.
"We knew Cardiff had a difficult away game in the week and travelled all the way here. We were at home, we had to take the game to them and we managed to get an early goal."