It's important to learn the followups for shine vs spacies (detailed above) - and it's just as important to realize when you shouldn't shine. A lot of foxes blindly throw out shines in the middle of combos and end up unnecessarily resetting the situation to neutral if they aren't prepared to cover the knockdown.
Fox's combo game on both falco and himself mostly rely on his strong grab game that leads into huge damage and stage positioning. In that way he's very different from falco, who loves to get meaty shine followups on spacies. Just changing that approach to the spacie matchup will get you a lot of mileage.
That said, Fox mainly just wants to get spacies off stage so he can edgeguard them. Shine is a super crucial part of this plan, and is amazing when used near the ledge. But in general your strongest punishes will come off grabs, and not shines. (Shines lead to tech chases which lead to grabs, but you get what I mean)
Learn when to shine and when not to!