I've been conducting a one-name study in the Twyman surname for the past 12-years, and am yet to come across a John Twyman who married a Mary Nicholls. Instead I think there's been a mix-up, as it's notable that the James Bristow who married George Twyman I's daughter Mary was the son of John Bristow & Micah Nicholls according to a couple of source. I think the two have just got jumbled up a bit when first put online, and it's spiralled out from there.
As for George Twyman I's roots in England, that's a bit of a mystery. Besides that he travelled to Virginia from London aboard the Recovery in 1677 around the age of 16, there's not much to go on for his roots. There are a handful of George Twyman's born/baptised in England (mainly in the county of Kent) in the early 1660s who might be him, but the ultimate proof has alluded many researchers for years. Hopefully an answer can be found in the near future.
Coincidentally, anyone researching the Twymans who would like to correspond & compare notes, as it were, please feel free to send me an email.
Thanks. :)
Simon