It's unclear for me if a mailed gift should be given on the day before an NPC's birthday or on the birthday itself, as they text you a "thanks" note on the same day of posting despite the post officer saying that it will be delivered on the next day.
I would recommend at least a tutorial bubble about it, but perhaps a "full-fledged" tutorial quest about gifting and the post office would be good, as it is a staple mechanic of the genre and could serve as a nice introduction to Yukio (since you already meet Hideyo at the auction).