Tumblr admins can see your dms with other Tumblr users. Discord admins will investigate you if youre reportedly hosting illegal content in any servers or in dms. Its literally no different from any other platform that allows 'private messaging'
By 'robots', as a mechanical being myself I mean an automatic generic '[X] support has received your report and are currently looking into it.' kind of thing where you have No Idea if any actual admins or mods are looking at any reports sent their way or if theyre just being left and forgotten or trashed.
For some reason its only different because... Instance admins are actual real people filtering reports and deciding what to do instead of bots? Which is what people should in theory want.