Just to confirm - while this gives you a free Imcando hatchet piece, the team confirmed you do not need to speak to Oak for the chance to find Imcando Piece Birds Nests to activate.
Once you have Tier 3, they automatically have a chance to drop through Woodcutting sources. You won't have missed out on any chances if you didn't speak to Oak before seeing this (just in case anyone panics!).