Seems very similar to this issue but a little different case. Uploading a custom emoji in /admin/customize/emojis seems to retain old emoji image in admin screen, after deleting and overwriting with a different image.
Reproduction: Upload custom emoji. Delete custom emoji. Upload different emoji image under the same name. Original emoji character will appear. Observed in v1.5.0.beta10 +44
Expected: On upload of a different emoji image, have the newly uploaded appear as the image.
I suspect cache validation is at play here – the updated emoji works great in the forum at large, and the updated appear as expected in the admin page on refresh, so I’d consider this pretty minor. However, it can be confusing to admins when replacing emoji sets.