Research appears to indicate no relation of Thomas Willis as the father the of Deacon John Willis.
. “THEORY - John Willis was born in 1610 the son of Thomas Willis who was born in 1575 in Fenny Compton, Warwickshire, England. “The Ancestry of John D. Newport” on Rootsweb lists a detailed pedigree of this family from a Thomas Willis born about 1450 in Priors Marston, Warwickshire to Thomas Wyllys born about 1575 in Fenny Compton, but does NOT account for a son JOHN WILLIS.
This family is DISPROVEN as relations to the brothers in Massachusetts. It is instead the family of George Wyllys of Hartford.”
More information to this is shown at:
https://www.wikitree.com/wiki/Willis-93