Kind of you to respond so quickly glad to be of help, you say of your sources: -
"Sir Thomas had 3 children - two daughters and then a son, John (Born 1570)."
The daughters' names of course do not agree with ODNB of the one daughter Elizabeth for whose existence there is substantive documentary evidence and for the ODNB son Edward your sources have a John and no Edward. That son John born in Romsey, father to Jane born 1614 looks just a little suspect to me as to him being Sir Thomas North's son. I would like to see 100% proved contemporary documentary evidence that he was so related.
The fact that Roger North 2nd Baron North's will 20 October 1600 says that, once all debts, legacies, and charges had been settled, ‘out of the Remaynder with some portion my brother Sr Thomas Northe, his sonne Edward Northe, his daughter my neece* Stutfeyld be reteyned’ seems to confirm that there were only two children, Edward and Elizabeth.
From the old book Athenae Cantabrigienses I mentioned a third child called Roger who died unmarried, probably at an early age.
Of course the compiler's of the trees on the Internet do not quote original sources as far as I can see, so as you rightly infer they must be viewed with caution.