Well Jupiter had been there all along. He was part of Archaic Tirad, and had been worshiped as far back as we have records. The Romans were deeply religious, and had dozens of priesthoods long before they had significant contacts with the Greeks. They also had hundreds of named gods and theoretically thousands of un-named ones.

For example they had multiple gods of the underworld: Pluto, Orcus, Dīs Pater, Febris, etc. These chthonic deities weren't necessarily well delineated. The Romans didn't worry much about a one true faith. When Lucius Catellius celebrated festivals for Dīs Pater that didn't mean he was choosing Dīs Pater over Febris. There's every reason to believe Febris' festival was celebrated on February 15th as usual. The Romans didn't worry about who was the true ruler of the underworld. When they were introduced to Hades, their thought was "cool, we've got similar gods, I bet he's one of those under a different name."

What they didn't have was a highly anthropomorphized view of their gods. They worshiped Jupiter, but they didn't tell stories about him. To the early Romans, Jupiter wasn't necessarily a human shaped being with sexual desires and the like. He was more a conceptual thing. So they were willing to adopt the Greek myths. Zeus wasn't imported into Roman worship, so much as a lot of Zeus' personality was grafted onto Jupiter.

Jupiter worship and practice in Rome didn't change to match that of Olympia. That wasn't particularly unusual, in Crete Zeus was known as Zeus Velchanos or Kouros. The Cretan worship was different from Olympia. Likewise Zeus-Lykaios had a very different worship practice. So there wasn't a single Zeus to adopt into Roman belief. And that was ok. Zeus could be a sky god to whom Eagles were important and he could be a light god to whom wolves (and werewolves) were important.

So when the Romans grafted Greek myths onto their deities, it didn't generally change much, other than they now had stories to tell about the gods. One thing that did change was that certain cults did gain in popularity over time. Libera was a very minor goddess associated with Ceres. Around 205 BCE she became identified as Proserpina/Persephone, Ceres became identified as Demeter, and some form of the Eleusinian mysteries began to be celebrated in Rome. But it didn't immediately supplant the existing rituals and celebrations. It just became something else they did as well. It took centuries, but over time Proserpina completely overtook and subsumed Libera.

So we talk of Romans adopting Greek religion it's important to recognize we aren't talking about a wholesale replacement. Mostly it supplemented existing beliefs. Where and when it did replace Roman practices, it took generations.

Sources:

• Yves Bonnefoy, Roman and European Mythologies
• Jörg Rüpke, Jörg (Editor), A Companion to Roman Religion