There is no one clear answer to this question. It will all depend on the situation. I think in most cases if the child is well established in his university studies they won't want to come to the US and, if so, not until they complete their university studies.
Unfortunately, with a divorce in the FSU, typically the children are with their mother and the father has little or no contact with them and has a new wife and family and limited living space. Having the child move in with them would be difficult. I'm generalizing here, and each situation is different, so please, no one take offense.
If the child is young, of course you should expect to bring the child to the US with the mother. In the age range you cited, there are too many variables to provide any useful information. You answered your own question best when you said that the best thing is to ask before things get serious.
I can tell you my experience, though it will have no bearing on 99.9% of the cases. My wife's daughter was 12 when I first met her. Had we decided to marry right away and come to the US, she would have come with us, no questions asked. Instead I moved there for a couple of years and by the time we decided to come to the US she was 16 and in her last year of school. It would have been much too difficult for her to come to the US at that point and it made more sense to leave her there to finish school. At this point the choice is to either let her stay there to go to university or come to the US. We have opted to bring her here, at least for a year, to learn English and get a taste of the US and the education system here. When we return to live in Ukraine in a couple of years, she will either come back with us and finish school there or stay to complete a degree here.
As you can see, at that age there are more options and ideas can change as things develop. So even though you and the fiance may decide something in the beginning, there is no guarantee that these plans will not change.