When an icon style is changed in Options ▸ LibreOffice ▸ View usually affects open windows immediately: this is e.g. the case for Writer, where all toolbars are repainted with new icons as soon as Options dialog is closed or settings are applied.
However, Start Center does not react immediately to the change. If a module is started (so that Start Center is closed), and then all documents are closed to return to Start Center, then all its icons are of course repainted to use new icon set. Looks like some notification is not watched.
Confirmed, its been like this since the StartCenter/Thumbnail views work at 4.2 for bug 61914