A shift in usage in the sixteenth or seventeenth century should do it. Dutch was still used to identify everything from the continental North Sea shore rather randomly up until the Anglo-Dutch wars. The word 'Hollander' was also in vogue for a while (used to identify all nationals of the United Provinces). Dialectally, you still find 'Dutch' identifying Germans (as in Pennsylvania-Dutch), but it's completely vanished from standard usage. There is no particular reason for this, especially given the Dutch do not self-identify as Duits.
Something as simple as an influential London printshop having an etymology-obsessed head typesetter could do it, I suppose.
Hollander has the problem, that it's a 'Pars pro Toto', it just as correct as calling every Britisher an Englishman. Netherlander would be more 'correct'.
Also Dutch stands for more than 'Duits', Low Saxon dialects in the Low Countries used 'Duuts' and other Dutch dialects also used 'Diets' (which became tainted due to WW II).
It's even debated where a line in the first stanza in our national anthem the Wilhelmus stands for. Fun fact the full lyrics of the Wilhelmus is comprised of 15 stanzas, however usually only the 1st and sometimes also the 6th stanza are song.
Here's the contemporary version (the original dates from 1568 (probably by Filips van Marnix van St.Aldegonde)) of the first stanza.
Wilhelmus van Nassouwe
ben ik, van Duitsen bloed,
den vaderland getrouwe
blijf ik tot in den dood.
Een Prinse van Oranje
ben ik, vrij, onverveerd,
den Koning van Hispanje
heb ik altijd geëerd.
the English (non melodious verison) translation
William of Nassau
am I, of Duytschen blood.
Loyal to the fatherland
I will remain until I die.
A prince of Orange
am I, free and fearless.
The king of Spain
I have always honoured.
Duytschen probably just refers to the people (which just happens to be what Duits/Diets/Duuts/Dutch all mean), but it could refer to the fact that William the Silent was born in Dillenburg (his father was count of Nassau-Dillenburg), where he inherited the principality of Orange and the other possessions of the Nassau-Breda branch, which just inherited Orange and other possessions of the house of Chalons-Arlay.
Also until the 19th century Nederduits (or variants thereof) was at times used for Dutch and Low German (Neder, where the English Nether comes from or is related to, mean Lower).