From Wiki:
History
The Malay people are believed to have originated in Borneo and
then expanded outwards into Sumatra and later into the Malay
Peninsula.[citation needed]
These people were descendants of Austronesian-speakers who migrated
from the Philippines
and originally from Taiwan. The main foundation of this
school of thought lies in the fact that the oldest Malay
settlements have been discovered in Sumatra and not in the Malay
Peninsula. This suggests an upward - south to north - migratory
route. Malay culture reached its golden age during Srivijayan
times. Malays practiced Buddhism,
Hinduism,
and their native Animism before converting to Islam in
the 15th century.
Etymology
According to the History of Jambi, the word Melayu originated
from a river with name Melayu River near to Batang Hari
River of today's Muara Jambi, Jambi province of Sumatra,
Indonesia. The founder of Malacca, Parameswara
was a prince of Palembang
which was once owned by a nation called "Malayu" back in the
seventh century. Yi Jing (635-713) clearly recorded in
his journal book a nation of name 'Ma-La-Yu' existed. According to
archaeological research of Jambi, large numbers of ancient
artifacts and ancient architectures of Melayu have been found with
photo evidence.
The word "Malay" was adopted into English
via the Dutch word "Malayo", itself from Portuguese "Malaio", which originates
from the Malay word "Melayu". According to one popular theory, the
word Melayu means "migrating" or "fleeing", which might refer to
the high mobility of these people across the region (cf. Javanese verb
'mlayu' means "to run", cognate with Malay verb 'melaju', means "to
accelerate") or perhaps the original meaning is "distant, far away"
(cf. Tagalog 'malayo')
Another theory holds that the name refers to the Tamil word
Malai Yur which means "Land of Mountains" (malai
means mountain and yur means land), a reference to the
hilly nature of the Malay
Archipelago.
Btw TS, whatever your book said is just one popular
theory
Read the various theories above.
Anyway, for most Malays in the past, they are simple folk who
fish for a living
And it is very common for them to move around looking for better
fishing grounds.
It is incorrect to assume that all Malays in Singapore and
Malaysia are here because they fled a war