Oh dear, this is what happens when I let things get buried in my inbox. Apologies.
The phrase "tender administrations" is an error; it should be "tender MINISTRATIONS."
Ministrations just means actions that serve or help; tender ministrations as a phrase generally means physical gestures of love, or sometimes a catchphrase for events performed by one person on another, i.e. during sex.
"Administration" is the management or functions of an office (including a political office)-- I think most people think of bureaucracy, paperwork, forms signed in triplicate, etc.
So the mistake of adding the ad to ministrations turns it from a phrase about sex to a clearly unintentional joke about impersonal, businesslike sex.
Poor fanfic writers. They should be more careful before they make me laugh that hard. I may sue for medical fees, I nearly fell over and broke something...