These boys evidently had a difference of sexual development (DSD), commonly known as 'intersex', though definitions of intersex do vary, so DSD is preferred.
It quite clearly says that both boys were brought up as girls until they reached the normal age of male puberty where they experienced male puberty, "her voice was cracking just like those of the neighbor boys"
This is actually fairly easy to understand and these are clearly not 'transgender' children.
Specifically there are a number of disorders that can result in a biologically male child appearing to be female at birth. For example 5-alpha reductase deficiency type II (5αR2D, or 5-ARD), reflects the fact that there are three separate 5-alpha reductase (abbreviated as SRD5) genes in the human genome. Type II is expressed in utero and is responsible for the virilisation of the urogenital tract forming the penis. A defect in this gene can result in a child being born with apparently female or ambiguous genitalia, a so-called pseudo-vagina.
If this is diagnosed at birth, the baby should be dosed with topical testosterone and raised as male.
However in less developed medical systems this may go undiagnosed.
What happens next is essentially normal human biology - there are small differences in sex hormone levels between the sexes until puberty, when male testosterone levels become about 20x higher than female, and similar effects occur with oestrogen.
As mentioned earlier, there are three genes involved 5-ARD and even without 5-ARD type II, 5-ARD type I can result in full masculinization at puberty.
This is widely reported see e.g. https://www.bbc.com/news/magazine-34290981 where a particular community in the Dominican Republic has a high rate of this disorder.
For two brothers in the same family to be born with the same genetic defect is hardly surprising.
Since SRD5 is a secondary sex hormone the normal testosterone production means that these men often have normal sperm production.
The tweet reports that David fathered a daughter (Jan Davey: https://www.edp24.co.uk/news/crime/emma-sandys-painting-stolen-in-great-yarmouth-sold-at-christie-1279442) with his wife, which should be another giveaway. Trans men can not father children. Trans men are biologically female and therefore can either be fertilised by a biological male, or are in some cases infertile. No trans man is capable of impregnating a woman.
There are plenty of cases, see for example:
See also this 20 page article on the subject: https://www.researchgate.net/publication/322596084_Diagnosing_sex_Intersex_surgery_and_'sex_change'_in_Britain_1930-1955
Not trans, and appropriating intersex conditions to try and make a point about 'trans' is often considered unethical by intersex people. See e.g. https://ihra.org.au/13651/isgd-and-the-appropriation-of-intersex/