What installer are you talking about? The game uses your browser's local storage to store your save file.
I think it's called Mega.nz or something. Every other game I've downloaded on Itch.io download immediately from the site onto my phone (Except Academy34, which directed to their website). When I try to download it redirects me to Mega.nz which I've downloaded from before but never had asked to store permanent data. Is it supposed to do that?
Mega is a storage provider that has been around for a very long time. They are safe to use. The reason for the pop up is because they use a technology where the file gets stored into your browser first and then gets generated as a file. It's different than the typical file download. They do this for privacy reasons.