Video of Tuchel shouting "Djed, Djed, Djed, wake up!" during a passing drill in training on Saturday went viral.
But the Tottenham Hotspur player, who made his World Cup debut as a substitute in England's 4-2 victory over Croatia in their opening match on Wednesday, said Tuchel's reaction reflected the standards expected within the camp rather than personal criticism.
"It's normal," Spence told TalkSPORT. "He's a great manager. He wants the best from his players. He demands high standards and for this tournament, we need to be ready, we need to be on it.
"Every session needs to be of the highest quality. That's what he demands. It's good. I wouldn't be the only one he says it to. It's part of the game."
Spence said the 52-year-old coach had fostered a strong sense of unity within the squad.
"I think he's a great manager, he's a great guy. Very detailed in what he wants to do. I've got great respect for him," Spence said.
"It's like what he always says, we're building a family, we've built a brotherhood within the team, everyone has one dream, one brain."
Aston Villa striker Ollie Watkins had mentioned Tuchel's yelling during a press conference on Sunday, but agreed with Spence that it reflected the coach's high standards.
"It was lucky it wasn't me," he said of Tuchel's outburst at Spence. "I think I made a mistake just before Djed did, but he ended up shouting at Djed, luckily.
"It just shows that he is a winner and that he is always driving the standards, making sure we are on it."
England next play Ghana on Tuesday in Boston.