Kean, who joined PSG on loan from Everton earlier this month, netted a brace on Saturday before Kylian Mbappe came off the bench to also score twice.
After PSG moved top of the table, Tuchel was happy with Kean, who made his third appearance for the club, but was quick to keep expectations low moving forward.
"He brings intensity to our game. It is his strength to bring intensity. He is an athletic player," the PSG coach told a news conference.
"He showed that he could help in matches at that level [against Nimes and Dijon]. We can't expect too much from him. He didn't play much at Everton. He has to keep improving."
Kean was replaced by Mbappe in the 73rd minute and the star France international delivered a double of his own.
Neymar assisted two goals and has been involved in eight against Dijon in Ligue 1 (four goals and four assists) – his favourite opponent in the top flight. He was involved in 15 shots (seven attempts and eight chances created), which marked his best in Ligue 1.
Tuchel was pleased with his side's performance at Parc des Princes.
"I'm happy with the intensity. It's never easy, we always play behind closed doors," he said.
"The players always have to find the momentum on their own because we miss the fans. It's completely different with 5,000, it's completely different with 40,000 in the stadium.
"It's hard to always have the spirit, the momentum without the atmosphere. Having the right attitude to attack, to do a high pressing.
"It's more difficult for all players and that's why I'm happy because we never lost this intensity."