Just to clarify, “favourites” and “saved searches” are different. I made a post about it:
I think @Lindsay’s comment is about notifications from saved searches and refers to the post below, which is in this same topic (since your post was moved):
So I really don’t know why your favorite notification wasn’t instant. Maybe it’s not “instant instant” but can take a few minutes to go through the system?
You could try contacting support like @Ksquared did and ask specifically about notifications from favorites. Let us know what they say!