You wouldn't have this problem if you were using $var[n] instead of $varn.

my @arrays = map { [ split /;/, $_ ] } @nums;
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But to answer your question:

my $num1 = "1;2;3";
my $num2 = "4;5;6";

my (@ar1, @ar2);

for (
   [ $num1, \@ar1 ],
   [ $num2, \@ar2 ],
} {
   my ($num, $ar) = @$_;
   @$ar = split /;/, $num;
}
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By the way, don't fool yourself into thinking the first argument of split is a text string. split expects a regexp.