An exclamation should definitely be accompanied by the exclamation marks, as you point out.
¡Aparta de ahí!
¡Cuidado!
¡Déjame en paz de una vez!
But Exclamar
has a wider meaning than "yelling, shouting or talking loud". One possible reason why there are no exclamation marks in the text there is because in that context "exclamó" is used as a synonym of "dijo", not "gritó". Realize that "exclamar" is
Emitir palabras con fuerza o vehemencia para expresar la viveza de un afecto o para dar vigor y eficacia a lo que se dice.
So what the word "exclamar" in that context means not that the person is yelling or talking loud, but emphasizes the way something is said. So instead of a LOUD
"¡Ciertamente este hombre era Hijo de Dios!"
it was a quiet
"(Wow) Ciertamente este hombre era Hijo de Dios"
that conveys surprise and respect.