The reason is that it happens every time a new emoji is being “lazy loaded” and the size attributes are being rendered.
Once it’s rendered, the issue doesn’t happen. But if you go through a topic with lots of replies and in which emoji are used a fair bit, you’ll constantly see this behaviour happens and it will make using Discourse impossible.
We managed to “fix” it in our custom theme but I think this should be addressed in the default theme as well, or even better, in the function that cook the posts as I can’t see a reason for those size related html attributes to be applied instead of using simple CSS.
I’ll add that every browser for iOS seems to be using webkit, so it’s going to be an issue mostly for apple device. I’m not an expert on it tho, so take this with a grain of salt. Some more testing would be required.