In a way that has to do with rules or instructions, especially in a religious or formal way.
The word rubrically can make people think of following rules or doing things in a very specific way, often in a religious or formal setting.
Examples:
The ceremony was performed rubrically, following all the rules.
She followed the recipe rubrically, measuring each ingredient carefully.
The students recited the poem rubrically, exactly as they were taught.
He dressed rubrically, wearing the exact clothes he was supposed to wear.
The robot cleaned the house rubrically, following its programming perfectly.
The soldiers marched rubrically, each step perfectly in time with the others.