That's because the (scalar) operator of an op= imposes scalar context on the lists and so only the last element of each list is affected:

c:\@Work\Perl\monks>perl -wMstrict -le
"my ($x, $y, $z) = (30, 40, 50);
 ($x, $y, $z) += (3, 4, 5);
 print qq{$x, $y, $z};
"
Useless use of a constant in void context at -e line 1.
Useless use of a constant in void context at -e line 1.
Useless use of private variable in void context at -e line 1.
Useless use of private variable in void context at -e line 1.
30, 40, 55
[download]

Raku can do these kinds of list operations; see Raku Programming/Meta Operators.

Update: I'm not aware that you can do this with pure lists in Perl 5, but it can certainly be done with arrays:

c:\@Work\Perl\monks>perl -wMstrict -le
"my @ra = (30, 40, 50);
 my @rb = ( 3,  4,  5);
 ;;
 $ra[$_] += $rb[$_] for 0 .. $#ra;
 print qq{@ra};
"
33 44 55
[download]

And via List::MoreUtils::pairwise():

c:\@Work\Perl\monks>perl -wMstrict -le
"use List::MoreUtils qw(pairwise);
 use vars qw($a $b);
 ;;
 my @ra = (30, 40, 50);
 my @rb = ( 3,  4,  5);
 ;;
 my @rc = pairwise { $a + $b } @ra, @rb;
 print qq{@rc};
"
33 44 55
[download]

or

c:\@Work\Perl\monks>perl -wMstrict -le
"use List::MoreUtils qw(pairwise);
 use vars qw($a $b);
 ;;
 my @ra = (30, 40, 50);
 my @rb = ( 3,  4,  5);
 ;;
 pairwise { $a += $b } @ra, @rb;
 print qq{@ra};
"
33 44 55
[download]

(The  use vars qw($a $b); statement quiets some warnings.)