The reason why Ultron is in White Vision's mind
I just re-watched Age of Ultron and noticed one scene that probably can explain why Ultron is in Vision's mind.
In the movie, Ultron printed Vision's vibranium body with the help of Helen Cho brainwashed by the mind stone in the scepter and he planned to upload himself into it. But Wanda interrupted the upload process by undoing the brainwashing on Helen. Then Helen stopped the upload at 42%.
In our regular computers, when an upload was interrupted, part of the data from the incomplete upload could still taking up space in the hard drive inaccessible to the user.
Here's comes my theory:
When Tony was uploading JARVIS into the vibranium body to create Vision, he probably didn't do a full factory wipe before uploading JARVIS into it. So part of Ultron's consciousness from the incomplete upload was stored within Vision's brain/hard drive as broken data inaccessible to anyone including Vision himself.
But when Vision's body was taken apart and reassembled, then the Hex Vision unlocked White Vision's memory with the mind stone created within the hex. It finally made that fragmented data of Ultron's base consciousness resurfaced.