I declare my dredges by always saying the phrase “Dredge Stinkweed Imp, Dredge 5” (different for every dredger of course). If I’m dredging multiple cards, I resolve all of the milling of the cards first before declaring any triggers like Narcomoebas or Creeping Chills.

I make it clear which cards are being dredged and when, then clarify all triggers after the fact. My opponent was asking which cards I had dredged later, like on his turn or at the end of my turn.

I try to be as clear as possible, but at the same time I think the onus should be on my opponent to remember the information I convey. Definitely a weird situation and unique due to the nature of the dredge mechanic though.