My children are young yet, but we have always emphasized to them that Christmas is about Jesus Christ, first and foremost. Like your children, they too will quickly remind anyone in their earshot who seems to have gone far afield, what Christmas is all about. They know "Jesus is the reason for the Season", and each year we do Advent candles, and Advent calendars with manger scenes on them, and we always have a birthday cake for Jesus on Christmas Eve, and we sing Happy Birthday to Him before we cut the cake. I hope they grow up with as deep a faith as your children have! Good job!
You're on the right track and you'll have some good kids. I was picked on by my siblings, (I'm one of six), when my kids were young because they thought I was too serious, (I am not a serious guy).
Now that all our children are grown and mine were the least trouble, the best adjusted, and the most successful of the whole gang, they concede that I was right. Start them out on Jesus and when they get old enough let them decide.
I advise anyone who will listen, "Don't start your relationship with your kids on some fantasy or lie. Jesus is real Santa is a symbol." It is surprising how well even very young children understand the difference.