I'll try my best to explain this, but first I’m curious to know what Chronicles you are looking at. I examined:

Froissart, Chronicles (Edited by Brereton, 1978) which has the event on p. 217 - Once the rebels entered London, "John Ball, Jack Straw, and Wat Tyler, with more than thirty thousand men, went straight through London to the Palace of the Savoy...belonging to the Duke of Lancaster (Gaunt). They quickly got inside and killed the guards, and then sent it up in flames."

Westminster Chronicle, 1381-1394 edited by Hector and Harvey, 1982. P. 5 "About four in the afternoon on [June 13] the peasantry, wrought up to a state of sheer frenzy, attacked the duke's palace of the Savoy, where they burst through every barrier and spared no article of value from destruction either by burning or by being flung out to sink in the Thames" Note - The Anonimalle Chronicle (1927) states that men from the city as well as the outside rebels participated in the destruction of Savoy.

Knighton's Chronicle edited by Martin, 1995. Pages 213-217: After executing the Archbishop and six others at the Tower, the rebels moved toward Savoy, "that mansion those servants of Satan cast down, burned, and reduced to ashes, with all its contents, except one bed and a few other things which its keeper gathered up while they were on their way. For in that house there were all the treasures of the said Duke John, with bed-hangings and other ornaments, with innumerable jewels...One scoundrel seized a fine piece of silver...but when someone saw it, and told the others they threw him and the plate together into the fire crying that they were zealots for truth and justice, not thieves or robbers.

The last one I have on hand is Chronica Maiora of Thomas Walsingham, edited by Preest and Clark, 2005. Page 123: On June 13, "they went in and out of the city and began discussions with the ordinary common people of London, about gaining their liberty and seizing the traitors, especially their pet hate the duke of Lancaster, they quickly and easily persuaded all the poorer people in the city to join in their conspiracy. And as the sun rose higher on that day and it grew warm and the rebels began drinking all the different wines that took their fancy out of the most expensive goblets, they became not so much drunk as mad...they encouraged each other to hurry to the Savoy, the house of the duke of Lancaster...to set fire to it and burn it to the ground. This would be an act of defiance of the duke himself, who they called a traitor, and would strike fear into the other traitors...they wanted it to be clear to the people of the whole kingdom that they were not doing this out of greed, and so they ordered a proclamation to be made that no one, on pain of death, should dare to touch anything or keep any of the things for their own use."

That being said – Nigel Saul explains it most succinctly in his biography of Richard II (pp. 58-59). The rebels of 1381 were part of a common tradition in England, where they claim to be supporting the King and against his corrupt ministers and advisers. “Foremost among these was John of Gaunt. Gaunt was disliked for his haughty demeanor and disdain for popular opinion. As a figure long influential behind the scenes, he made a convenient scapegoat for the accumulated failures and errors of policy in the 1370s and early 1380s.”

Richard II ascended to the throne as a minor in 1377, and John of Gaunt was a major political player that orchestrated a good deal of the royal policy. Further, one of the major catalysts for the revolt was the excessive taxation, most recently the poll tax of 1381. The poll tax drew excessively on the lower elements of English society, and these were the same people who made up the rebels (Dobson, The Peasant’s Revolt of 1381 pp. 1-31). Gaunt’s extensive property, jewelry and general flaunting of his wealth made him a ready target for the distressed (and probably drunk) rebels. And in the chronicler’s descriptions, you can see how the rebels tried to assert the justice of their cause, and claim to be for the King and Justice. They tried their best to claim that their attacks against the Archbishop, Gaunt, and other advisers of the King were just that – attacks on evil counselors.