How does Startup Manager block startup apps?
Some research indicates that this is most likely done by revoking permissions to the apps you specify. Specifically, the app needs android.permission.RECEIVE_BOOT_COMPLETED in order to run at startup.

However, while this is the most likely situation, I can't speak for the exact functionality of Startup Manager.

Additionally, if you're concerned because the app's description isn't clear about how it works, you can alternatively use Autostarts, an open-source Android startup helper tool which controls which intents actually get sent to which apps.