Because the Tesseract activated when the Red Skull held it
Despite what everyone on Earth believed, Schmidt didn't perish from the Tesseract. Instead, he was teleported to the planet Vormir, the home of the Soul Stone, as punishment for his abuse of the Space Stone's power. Due to loving no one but himself, Schmidt was unable to take control of the Stone for himself and the Stone cursed him into becoming its guardian for over seven decades, rendering him unable to escape the planet and forcing him to advise seekers of the Stone what price they needed to pay to obtain it as well as making him immortal and able to immediately tell who came to Vormir.
Source: Red Skull > Biography > Stonekeeper > Advising Thanos (1st Paragraph)
from the above what happened was that when he held it what happened to the Red Skull was punishment for abusing the power of the Space Stone (what the Tesseract is the container of) since Red Skull used it as a battery for weapons but as per the wikia entry on it
The Tesseract is a cube which contains an Infinity Stone, representing the fabric of space. If used correctly, the Tesseract can open gateways to any part of the universe and provide interdimensional travel.
Source: Tesseract > Capabilities
why did it look like he disintegrated? because it's cool. though seriously it was probably because he was being forced though the portal against his will unlike the times Loki, the Chitauri or Thanos used it's power.
Red Skull's state on Vormir, as indicated in the first quote, seems to be the result of him trying to take the Soul Stone for himself and not having anyone to love (to sacrifice), was punished again.