Lucasfilm owns the IP itself, so that's what Disney inherited when it acquired the studio. Paramount's distribution rights go back to the original deal George Lucas made with Michael Eisner (then at Paramount) back in 1979. Pretty much every studio turned down Raiders when Lucas shopped it around, and a stumbling block was that they simply didn't believe that Lucas could produce the film for $20 million he claimed he could. The script read like an expensive epic, and Spielberg had a reputation for going overbudget before Raiders. Lucas and Spielberg were committed to deliver under the promised budget as part of the deliberately "down and dirty," television-like schedule they intended to shoot Raiders on, but it was probably hard to imagine on a financier's part. In the end Paramount agreed to finance the movie on the condition of major penalties if it went overbudget as well as perpetual distribution rights to the movie and any sequels.
That means that when Disney acquired Lucasfilm over thirty years later, they weren't even left with the rights to distribute a fifth Indy. About a year later Disney cut a deal with Paramount to secure the distribution rights to future films, with Paramount retaining the rights to the original four and still getting some sort of financial participation on what comes after. You gotta hand it to Eisner -- that deal he made has been a license to print money for Paramount for 40 years.