Parent Katherine, who has two sons at the school, said the change in approach was initially a shock.
"It was a bit military - some people called it draconian," she said.
"But sometimes you need that shock to kind of get everybody singing from the same hymn sheet."
Mr Ebenezer said he wanted to make Caldicot School one of the top 20 in Wales.
"It's about doing the right thing," he said.
He said his focus was on "high standards of uniform and appearance, punctuality, attendance, behaviour, attitude" and said prevailing approaches to behaviour were misguided.
"It's definitely too soft. I think people confuse strict with nasty," he said.
"Strict is no nonsense - you do this, this happens. No means no, it's not nasty.
"I think at the moment we are indulging and we are hiding behind words like wellbeing and safe spaces and it's making things unsafe and is damaging people's wellbeing."
Mr Ebenezer said he and his staff needed to be "allowed to do what we need to do and not be inhibited by ridiculous bureaucracy".
"We will be safest, happiest and flourish most when we bring back firm discipline, strict boundaries and we can get on with it," he added.
The Welsh government said: "Schools should be safe spaces for learners and staff and all education settings in Wales have a legal duty to provide a safe learning environment. It is up to schools to set their own detention policies.
"We are working with partners to develop proposals to improve behaviour, including a National Behaviour Summit which is planned for the spring."