Illustrator provides two ways to access Next Object commands:
1. From Select menu
2. From the context menu, Select submenu

However, they work differently.

If you use #1 commands, they behave as expected — Ai properly selects the objects at the current scope level (if we are isolated), by stack order in Layers.

But if you use #2 commands when isolated...
These commands, despite having the same names as the command from the top bar menu entries, rely on the object being clicked. But even knowing that (and it’s not an obvious thing to figure out), the result is weird.
Illustrator then selects everything in the scope. This is not at all what we need! Take a look at the attached GIF, please. Illustrator treats the parent as the next object in the hierarchy. It is expected to select a child instead.

BTW, notice that the variant #1 is missing two commands the context menu provides: First Object Above / Last Object Below — for no apparent reason — and we can’t assign hotkeys to these because of it. Here is a feature request to honor the parity: https://illustrator.uservoice.com/forums/333657-illustrator-desktop-feature-requests/suggestions/46741999-add-first-object-above-last-object-below-command