[quote]Can they even do this?[/quote] Clearly they can if they did lol. Whether or not it's right is another thing. Which leaderboard is it? Rule changes can occur in response to new runs if the changes make sense and it's not just being done to protect records.

Generally speaking it makes sense to time things when you gain control of your character, and lose control of the character. So starting time at level select doesn't make sense either (though I don't know anything about this game).

At a glance it looks like the transition to the next level is maybe slightly slower the the mod's run, but it could be a difference of frame rate. Either way if a timing change is implemented, all runs would have to be re-timed anyways. So if you beat their run, but the new timing ruling allowed their run to tie with yours, then there is some kind of hardware difference or loading difference not being taken into account. Which is more of a reason to not end time on a level transition, so you're correct.

Also I'm surprised that a run that short with times that close that milliseconds aren't used.

Just reach out to both mods and ask them to clarify the rules and to add milliseconds for the runs. The rules for that category are incredibly lax and poorly written even for a mobile game. If that doesn't work you can use the support hub I think for further action (I've never used it personally so idk) or reach out to site staff on discord.

Contacting the site staff is the most useless thing you can do. Talk about adding milliseconds, since in this case they are necessary, falsification and abuse are also clearly visible

Although it probably doesn't make sense, since ILS is not the most important part of this game

If you are talking about direct influence, then you should discuss this problem with @starsmiley, however, perhaps you can ask someone from respected players to help you. The game is not very popular and ils is usually ignored.