Yes, that will work if both strings are found on the same line, but does not guarantee that the second string comes after the first string.

I have amended my program to take care of this:

use Modern::Perl '2014';

my $first  = qr/STRING/;
my $second = qr/MAGIC/;
my $first_pos;
my $first_sub_pos;
my $second_pos;
my $second_sub_pos;

while (<DATA>) {
    do { $first_pos  = $.; $first_sub_pos  = $-[0] } if /$first/;
    do { $second_pos = $.; $second_sub_pos = $-[0] } if /$second/;
}

if ( $first_pos and $second_pos > $first_pos ) {
    say "Success! STRING at $first_pos followed by MAGIC at $second_po
+s";
}
elsif ( $first_pos
    and $second_pos == $first_pos
    and $second_sub_pos > $first_sub_pos )
{
    say
"Success! STRING (char: $first_sub_pos) followed by MAGIC (char: $seco
+nd_sub_pos) at $first_pos";
}
else {
    say
"Failure! (STRING: $first_pos / $first_sub_pos - MAGIC: $second_pos / 
+$second_sub_pos)";
}

__DATA__
First line
second line
here is the STRING
empty text
the STRING again!
followed by the  MAGIC word
more emptiness
Oh no! the first STRING again
sadness
did we look in vain?
Ah, STRING and MAGIC success
MAGIC and STRING failed
[download]

Just add and delete the last lines of the DATA section to see the various possibilities.