I don't think it is a "chief parent" thing, but I do think that it's a common issue with stepparents (particularly stepmums but any situation where the SDC usually live elsewhere and the stepparent didn't have children before) thinking of the SDC as unrelated-to-them visitors who can be fun or cute or charming sometimes, but mostly, if they are really honest, (especially once they are over the "cute" stage - about 4) feel slightly resentful of them encroaching on their time with their DP and, later, on their time with their new family.
Of course, they'd never express this to the SDC, and I really don't think it comes from any place of malice or is even actually that conscious, perhaps it's even a source of guilt, but it does cause problems because it's like she puts a barrier up to actually interacting with them, isn't really invested in putting in the boring work of getting to know children in that in between age (you can't instantly charm them like toddlers, you can't chat to them on an adult level like teens) - perhaps, again, not because of any conscious resentment but just because the relationship doesn't come as easily to her, or even a sense of not wanting to try and take over as "mum" when they already have one, or respect for not wishing to encroach on their DP's time with his children, who he obviously does have a relationship with which he will put time and effort into (hopefully!) And this can work to an extent for many years although there will be occasional clashes over the way he deals with them, but it is usually minor in the scheme of things.
Where this causes issues long term is if and when the stepmum and the new partner decide to have children together. If the disparity is not resolved, it can lead to a strange situation for the stepmum where she ends up feeling almost left out or pushed out of her own pregnancy and new motherhood. Her partner has been here before, but it's all new for her. His parents/family are perhaps less excited than hers are or than she'd like which is suddenly disappointing. His children are expecting to be around and involved with the new arrival whereas all of her friends having children and everything she reads about having your first baby emphasises the importance of private time to establish your new family. She has a different task which nobody talks about: that of blending her new motherhood (which is a profound change as I'm sure any mother will agree) into an existing family which she's never really felt was "hers", which she's always been on the fringes of, which, perhaps, she has never felt really existed and yet here it is, invading into that space.
I think stepparenting is hard whatever the situation, FWIW, but this particular set up makes it harder because of the constant cognitive dissonance of the SDC being both part of her partner's family and not part of her family, where she and her partner are the family. To release this and make things easier (not easy, but easier) it's important to accept the SDC as being "hers". Not her children, of course, as they already have a mother, but hers in the same way that her nieces or nephews or godchildren are hers: They are important children for her to develop relationships with, they are members of her family directly, not just through somebody else. Instead of being a mother of a new baby with some siblings, she's a mother of the third baby in a family and needs to approach family life in that way. It does mean that she misses out on many of the experiences of the first baby thing, which can of course be difficult. It does mean that she has to accept that her partner is likely to have different discipline standards to her (though this is an issue for all parents, I promise!) and has the added complication that he's likely to have been enforcing different discipline standards for years before the new DC came along which can be hard to change. It's also difficult to appreciate as a mother of young DC how things can change and your standards can wane as the DC get older - you don't get that slow slide into more TV and fewer vegetables with stepparenting, because your partner has already gone into those habits while you're still in the idealistic pre-parenting or new-parenting state of "MY children will never... etc etc" and that can be difficult to adjust to.
What's important and what will make the situation easier - Open mindedness (willingness to see how things work out), being more laid back than you'd need to be in a more traditional set up, accepting that your own DC are one of three or four rather than one of one or two "plus extras", and embracing that even if you didn't want a large family, putting time and effort in to build relationships and get to know SDC personally, spend one on one time with them, grieve privately for the experiences you miss out on by doing it this way, expecting it to be hard, and not beating yourself up for that! If you're struggling with still seeing them differently try asking yourself "When my 2yo is 6/8/10, imagine he has a baby sibling. How would I deal with the situation then?" You can end up with the best of both worlds by embracing the large family thing when they are there and then being able to appreciate the simplicity of a smaller family when they aren't, but it does take work and effort to build a relationship with the older ones in a meaningful way, and you can't get too hung up on worrying about encroaching on their time with DH or being seen as trying to replace their mum. You'll never replace their mum no matter what, and time with DH is now time with you, and with their younger siblings, too.