Use a regex to capture what you want rather than trying to deal with end effects splitting. Note the use of a __DATA__ section in the sample code - it was added to Perl to facilitate posting code to PerlMonks.

use strict;
use warnings;

while (<DATA>) {
    my ($var1, $var2, $var3) = /"([^"]*)"/g;
    
    print "Var1: $var1\n";
    print "Var2: $var2\n";
    print "Var3: $var3\n";
}

__DATA__
"value 1","something else","other stuff"
"asdf123","omg","hope this works"
"more tests","testy","blah"
[download]

Prints:

Var1: value 1
Var2: something else
Var3: other stuff
Var1: asdf123
Var2: omg
Var3: hope this works
Var1: more tests
Var2: testy
Var3: blah
[download]