Officers and volunteers are continuing to search the Isle of Wight for the Glasgow uni graduate who was last seen on Sunday.
Now, her mum Julia, dad David, sister and brother have joined the operation to find her.
Mr Johnson said: “It’s totally out of character for Rosie to go missing for any period of time.”
Her uncle, Labour Member of the Scottish Parliament Daniel Johnson, urged anyone with information to contact police.
Rosie’s family’s arrival comes as Inspector Andy McDonald said he did not believe the 22-year-old was the victim of a crime but confessed he was “concerned” for her safety.
Police were alerted on Monday when Rosie failed to show up to work at the Little Canada adventure park in Wootton.
An employee at Little Canada said Rosie was a “popular girl” and also added her disappearance is “totally out of character”.
The staff member, who did not want to be named, continued: “I think her boyfriend is out looking for her.
“She’s a pleasant girl. She’s come straight from uni and she’s a nice young woman. As far as I’m aware she’s popular and this is totally out of character.
“It’s totally out of character for Rosie to go missing for any period of time”
“I do know her boyfriend – he’s not in today, I think he’s out looking for her. Both live here.”
Rosie is described as having mousey brown hair and is of slim build.
When Rosie was last seen, she was wearing a dark blue puffs jacket and trousers.
She is believed to have left the adventure park with no money or phone.
A Hampshire Police spokesman said: “If you think you might have seen Rosie since she went missing, or have any information about where she might be, please call us as a matter of urgency on 101 quoting 44190217273.”