So... "Provincialism"?
i.e. "I'm from Gaul, I'm a baws, you Iberians all suck", "Those dirty Iberians, coming and taking our jobs", "Gauls make the best fighters"
Honestly, I'm not sure how, from my understanding the Romans had always tried to disintegrate tribal groups by distributing their people around, making it hard for any group to have a long-term attachment and ownership of the history of a region, which nationalists tend to use.
Plus, nationalist tendancies in the Empire would probably be seen as rebellious tendancies, and risks of rebellion which must be quashed.
If instead you're just interested in a sense of provincial pride, then I can see it happen - I actually think Iberia might not work for this, but Africa/Gaul/Italia could all have their own flavours.
Gauls - Hard pressed, resilient, perhaps with some weird obsession over Julius Caesar and Vercengetorix.
Africa - Resilient again, instead focusing on the cruelty of the desert, and their ingenuity at making the Atlas mountains bloom.
Italia - Conquered everyone, we're the best, we're the richest, and frankly, why should we subsidize the provinces? More aloof.
*shrug* I don't know how realistic this is, but there are some thoughts.