It will never update without you pressing update, unless you previously accepted a distribution upgrade update. But it sounds like you’ve refused that.
AFAIK the MyOSMC updater uses python-apt. Unless it’s been configured to use a different location to store the downloaded packages, they’ll be in /var/cache/apt/archives. Perhaps @sam_nazarko can confirm.
Running sudo apt-get clean will delete the files in /var/cache/apt/archives.