Depends on the region! Iberia wasn’t pacified until the late 1st century BCE, so up until then, there would have been intermittent wars between Roman occupiers and Iberian tribes. But for a good ~200 years, the only war Iberia was involved in was the civil war in 69 AD (nice), which was fairly short and largely didn’t take place in Spain. There was also a rebellion a few years before that, though localized to only part of Iberia. Ironically, Italy was hit much harder in 69 AD. Suffering from success - or at least importance!

Starting at the Crisis of the Third Century, in the, uh, 3rd century AD, civil war became a much more common occurrence, but even then, large-scale invasions and destruction (minor incursions of raiders and pirates aside, and civil wars, which were generally much less destructive than invasions) wouldn’t visit Iberia until, as you noted, the Visigoths arrived. So you could consider it to have had a good ~400 years of peace - Pax Romana! Or ~300-350 if you want to count from the rebellion in the 60s.

Why so many people submitted for so long to Roman rule, and even identified themselves as Romans - was that Rome did bring peace for most people, if not always a just one (and with the threat of war should their notion of peace be interrupted) for the first ~200-300 years of the Empire. With the notion that everything you have and everyone you know could easily be swept away in wartime, with tribal migrations often having a component of what we would today regard as ethnic cleansing, peace becomes… much more precious.

Most provinces experienced something similar - though border provinces always had some amount of cross-border raiding to deal with, and penetration of the borders became more common in the Crisis of the Third Century. Largely, though, the inner regions of the Empire enjoyed peace, even as the institutions of the Empire fell apart under the strain of incompetent elites and outside pressure, and it wasn’t until the mid-4th century AD that war really started to roll over ordinary people like the pre-Roman days.

Of course, by that time, the Empire itself had become such a shit deal that many ordinary people preferred the invaders to the Romans, unlike at the height of the Empire, when it could rely on the loyalty and even participation of poor folk in repelling invaders.