整
should be used after the measure word, so 三百八整人
is not correct.
However, 三百八人整
is weird too. 整
is usually used at the end of the phrase to prevent from adding new numbers to change the whole meaning, especially in financial affairs. Such as
三元
-> you can change it to 三元五角八分
三元整
-> you can't change it to 三元整五角八分
, which is wrong expression.
Originally 三百八人
can't be changed to 三百八人零点五人
and so on, so need not to add 整
after that.
BTW1: It also can be written as 正
in financial affairs.
BTW2: As @user58955 said, 三百零八人
is more natural than 三百八人
.
三百八
definately means380
, but三百八人
is ambiguous.