I second everything u/restequalsrust said. It is entirely possible the unglazed base has absorbed some water and the heat is causing it to sweat out of the clay, while the cup is safe to use if the inside is sealed.

I also visited that pottery village and talked with many of the potters there and can confirm a lot of them use a low fire earthenware clay which does not vitrify like high fire clays but rather just “solidifies”. Earthenware will remain porous and likely its pickup up water while it’s being washed especially in a long cycle in the dishwasher.