The red dots on the right side of the screen are indicating that Yakihonne can't connect to those relays. That might explain why you aren't seeing notes that aren't already in the app's cache.

Primal doesn't read directly from relays, but I believe it still writes to them directly, assuming it can connect to them. So, when you post on Primal, notes should appear on other clients that read from those relays right away. Again, though, the client has to be able to connect to those relays.