Not easy to answer that because it really depends on what defines a gene family, and how far apart they have derived from their common ancestor. Obviously immediately following duplication you will basically just have two identical copies of the exact same gene. For all intents and purposes you still have the same gene, they don’t so much belong to the same family as they really just are the same gene twice.
Then when they start to diverge, if you go merely by homologous relationship based on nesting hierarchical structure in sequences of similar genes, then yes they’d be classified as belonging to the same homologous family under that definition.
But there can be functional or mechanistic differences between genes that derive from common ancestors that make them be classified as belonging to independently evolved, monophyletic sub-families, within a larger superfamily of genes. Pretty much directly analogous to how you can have independent families of organisms, say primates and lagomorphs, within larger clades like mammals.
Well they show no signs of being consistent in what they think of diverging duplicate genes. If you show them two genes with a sequence similarity of about 80% they’ll call it highly conserved and insist it’s only a sort of protein “microevolution” and that they still just perform the same function (yadda yadda yadda). You show them two proteins that have diverged to 30% sequence similarity they’ll suddenly turn around and insist there are huge an unexplained “information jumps” that couldn’t possibly evolve.
Take one look at Gpuccio’s ridiculous figure that Bill keeps posting to see what I mean.I’ve drawn a phylogenetic tree on it and attempted to put the the approximate divergence times to scale (mouse-human is 90 mya according to timetree.org):
Look at that gap. Gpuccio wants to see all the intermediate stages in the divergence of those gene-sequences, otherwise it’s a huge gap without transitionals, and that means the species, wait sorry I mean functional information (FI), must have been popped into existence with magic!