When Louie uses Gyro's Time Tub to steal lost treasures from the past, a mysterious storm in the present sends all of space and time crashing down onto the mansion.
Life is like a hurricane in Duckburg as the El Pato Tropical Storm strikes the city, forcing the residents of McDuck Manor to prepare. All except Louie, who reveals to Launchpad that he "borrowed" Gyro Gearloose's Time Tub as part of his latest get-rich-quick scheme: with his new "Time Treasures" venture through Louie, Inc. he goes back in time to find famous lost treasures at the exact moment before they were lost, avoiding risking time, resources, or lives navigating dangerous temples. He demonstrates by taking Launchpad back in time to the caveduck era and taking an artifact. Unbeknownst to him, the time tub also zaps one of the caveducks, named Bubba, into the present, to be discovered by the rest of the family.
Huey, who has been studying caveducks as part of an effort to get into the Junior Woodchuck Guidebook, tries to use his knowledge to learn more about Bubba. To his annoyance, Bubba does not exhibit much in the way that matches anything in his research, showing a love for modern clothes, chili cheese dogs, skateboards, and rock music. Meanwhile, Mrs. Beakley tries to get Della to implement some tough love with her children as they get up to their usual antics. Della, however, prefers to encourage their activities, claiming she should be supportive.
Louie's adventures in time travel soon go awry when it turns out the Tub creates a time vortex, which combines with the hurricane to form a "Timephoon" that teleports figures from history such as Benjamin Frankloon into the present. Gyro, who was pulled through the space-time continuum into McDuck Manor, reveals that using the Time Tub creates an after blast that can bring people along with it: the Timephoon dumps pirates, old-time bicycle performers, ninjas, Spanish (or French) freedom fighters, cowboys, and even a dinosaur onto the McDuck Manor grounds, forcing the family (with Bubba's help) to deal with them. During the massive free-for-all from people across time, Mrs. Beakley reminds Della that she needs to keep an eye on her kids so their antics do not lead to bigger problems, case in point. Huey tries to keep up with monitoring all of Bubba's anachronistic behavior, including taming the dinosaur aptly named Tootsie by Huey.
Things take a turn for the worse when the timephoon's lightning starts blasting members of the family into the past. While looking for the Time Tub, Della discovers Louie and Launchpad in the middle of trying to put the treasures back, much to her anger. As the timephoon starts sending the rest of the family through time, Louie figures out how to use the Time Tub to send everyone back to the proper points in time, fixing the time vortex and bringing his family back to the present. Louie apologizes for his selfishness, and most of the family is happy to express forgiveness. Della, on the other hand, angrily points out his antics put everyone's lives at risk, and finally puts her foot down by grounding him from any more of his schemes. Mrs. Beakley assures Della that a little tough love now will make her children better people later.
Later, while cleaning up the Manor grounds, Huey finds out his report for the Junior Woodchuck Guide was rejected due to how outlandish it was, much to his disappointment. Scrooge discovers one of the heirlooms of Clan McDuck, a club from the caveduck era, is missing. Remembering Bubba was the one who last used it, the kids wonder if he may have been their ancestor due to his intelligence and strength, but shrug it off. In the past, however, Bubba carves himself a hat much like Scrooge's.
When the ninja who suddenly attacks the family in the the mansion after making his appearance due to the lightning strike of the Timephoon disappears and leeave a log in his place, it is probably a reference to the substitution jutsu used by the leaf shinobi from the Naruto series.