I always tuck in a 'dress' shirt (i.e. one that has irregular tails front and back designed to be worn with a tie). When in the kilt I always tuck in the top garment, shirt, polo-shirt etc. except for a knitted jersey or sweater.

However, if I am wearing what I call a cuban style shirt, which has a shorter bottom edge all of the same length, short sleeves, and a collar designed to be worn open I keep it untucked from my chinos, as that is how the shirt is supposed to be worn. I don't wear that style of shirt with my kilt but I would imagine if you did it would need to be untucked.

When I was a wee boy (under seven years old), my kilts had a cotton bodice and were designed to be worn with shirts which had a very short bottom edge (no tail) untucked.

Anyway just my two bobs worth!