Bethany and Jacob/Esau's winning run were on Hard mode, while none of the alt character runs were. My very first run of Mega Satan was with Bethany after initially unlocking her, and did not produce a void portal, while my first and only Mega Satan clear with Jacob/Esau did - the latter case may be down to random luck or may be that clearing Mother is a condition to the bolstered chance. Most bosses appear to be untouched and I'm not entirely sure of whether there's conditions such as specifically being on alt characters or unlocking one of the new areas, but in 10-for-10 successful runs on alt Eve as well as one each with alt Bethany, alt Cain, alt Apollyon and alt Forgotten Mega Satan dropped a void portal every time.