As a person who has been on the receiving end of this at a young age, I'll offer you some perspective from the point of view of the child. It may not be exactly what you're looking for, but it is the other side of the coin.
Generally speaking, this situation depends on how long you've been seeing said person (leaving the child in the significant other's care), how you present the information to the child (first introduction) and how old the child is (leaving the child in your significant other's care). I suppose it could also come down to how old your significant other is and how well he or she deals with children.
In my case, this first happened to me when I was about 8 years old; I met my mother's boyfriend and he was a pretty cool dude, my mother was candid about it, she told me that she was seeing him and that she really liked him, and in that way, the information was conveyed quite well. I don't think she left me in his care for all that long at any point in time though. Maybe six months into their relationship she had him watching me for a day while she was at work, but never more than that and never over night. When I was left under his care, I was mostly off doing my own thing so I didn't have much in the way of contact with him. I didn't really mind it though. Probably helped that he was a pretty stand up guy for the most part.
I suppose it depends on the kid though, each child is different and can react in different ways to the stimulus.
As a grown man, meeting my mom's current boyfriend wasn't the best, but that's because he's a dick. Still don't like the man.
