However, I'm still not sure how it ended up with the pattern it has with a red hen and a white rooster.
White silkies are usually recessive white, which can hide any pattern underneath their white.
That's the answer.
A chicken with two copies of the recessive white gene will look white, but it still has all the other color genes a chicken would normally have. So it's genetically gold or silver (but you cannot tell which.) And it is genetically chocolate or not-chocolate (but you cannot tell which.) And so on, for all the other color genes.
When you cross a chicken with recessive white to one without, the chicks get only one copy of the recessive white gene--and because it's recessive, you don't see any white from it. So you can see the effects of all the other genes each parent had, that they passed on to the chick.
Recessive white chickens are like a box of surprises, as regards the colors of their offspring