I am not sure if this John Willis is different than the guy with four brothers but the one mentioned in the book "The original lists of persons of quality; emigrants; religious exiles; political rebels; serving men sold for a term of years; apprentices;..."
Was TRANSPORTED from Gravesend, London, England to St. Christophers near Barbados on the Paul in April 1635
Transported as in was convicted of a crime and sold into bondage, not "Immigrated"...there is no mention of the brothers, and I am not sure how or if he got to Mass. from the Caribbean.
https://archive.org/stream/originallistsofp00hottuoft#page/50/mode/2up
I wouldn't make the assumption that "transported" = "criminal". Mr. Hotten copied the original ship's manifests verbatim, and their word usage is often very sloppy. If there is a mention of "oath of allegiance" and/or "conformity (to church of England)", they may have indentured themselves (having no money to pay passage) but they're probably not convicts.
There are sources that will tell you exactly who *was* a convict (and often what they were convicted of), such as:
The Complete Book of Emigrants in Bondage 1614-1775, by Peter Wilson Coldham
Bonded passengers to America, by Peter Wilson Coldham
Criminal ancestors: a guide to historical criminal records in England and Wales, by David T Hawkings
To Maryland from Overseas, by Harry Wright Newman (Maryland-specific)
Note: it's much easier to find records of persons deported to Australia, as the Aussies have made no bones about having "convict" ancestors.