I looked at free BMD, can't find a marriage (1910 onwards) using the surnames JOHNSON and TUNSTALL (including spelling variations)
Can't find a birth of a John JOHNSON, mother's maiden name TUNSTALL from 1911 onwards (when the mother's maiden name was included in the index)
Q1 1918 Tynemouth District has a marriage for a John HAND and Mary TUNSTALL (no middle name given)
North Tynemouth Registrars site show their local reference as C-5 9, 301 which indicates they were married at St Alban Earsdon
A marriage cert/entry in the parish register would confirm/deny if this is the right Mary Tunstall you are looking for.
Q1 1919 Tynemouth District has a birth for a John HAND, mother's maiden name TUNSTALL
A free search of the 1939 register for the surname Hand specifying Seaton Valley U.D. (which included Shiremoor) shows 2 Johns (b1893 and b 1919) and one Mary E (b 1895) Clicking on each of those entries in turn suggests they were all in the same household but you would need to pay to see the full record.
Can't explain why this lady would sign her name as Johnson on the letters you spoke of , but it would appear that there was no official marriage in England & Wales for Johnson /Tunstall and no birth registered to correspond to the child.
Boo