This Aesculus parviflora has new leaves growing from what look like bud scales to me. This seems unlikely to be the case, so I'm interested to know what I'm really looking at here. I saw the same thing happening on a Fraxinus ornus 'Arie Peters'. This is a young tree, still with its Parks Board label, the buckeye is not a young tree.
I don't know how I would tell. In the third buckeye photo, the branch going off NW, the leaf petioles look like they started as one of these structures, haven't yet become fully round. Looking at that photo, the leaflets seem to be different in the veining and the margins. Maybe they're not leaves. I'd even guess they were stipules, but Aesculus are not supposed to have those, according to two websites.