The J language isn't particularly strong in string manipulation. You can get an easy solution this way:
reverseWords =: (,' '&,)&:>/@:|.@:;:
reverseWords ' one two three four '
four three two one
but it sort of feels like cheating because of the use of the
;: verb which breaks a string to J tokens.
A solution without this cheating is (I have replaced the tab character with a hat for legibility):
reverseWord1 =: [:(,' '&,)&:>/@:|.@:-.&a:e.&' ^'<@}.;.1]
reverseWord1 ' one two three^four '
four three two one
Another solution is:
reverseWord2 =: [:}.@;@|.e.&' ^'<@(' '&,@}.`(0$])@.(2>#));.1]
reverseWord2 ' one two three^four '
four three two one