I assume like with similar services you need to give Gmail API access which does afford the possibility of them reading all your emails (although I assume they don't).
It's unfortunate that the Gmail API doesn't offer more granular permissions that would actually not allow Adios to access email contents. Even if I trust you, any breach of Adios could mean that my email contents are public.
Not bashing the service at all though. I'm a current user of Boomerang which has the same caveats.
The way it works:
1. creates a filter that filters your incoming emails into a hidden gmail label
2. at your chosen times we use the gmail api to move the emails back in to the inbox.
Adios never ever accesses the content of your emails, for any reason.