This seems like an interesting bug to me, both 5.6.1 and 5.8.0-pre affected. Look (I've condensed your test case a bit for use it from a single file):

package Foo;
sub TIEHANDLE { bless {}, $_[0]}
sub READLINE {return "foobar\n"}

package main;
#use Foo;
tie(*TEST, Foo);
chomp($data = <TEST>);
print join(", ", map { ord($_) } split(//, $data)) . "\n";
chomp($data);
print join(", ", map { ord($_) } split(//, $data)) . "\n";
[download]

results in strange output

102, 111, 111, 98, 97, 114, 10
102, 111, 111, 98, 97, 114
[download]

but following:

package Foo;
sub TIEHANDLE { bless {}, $_[0]}
sub READLINE {return "foobar\n"}

package main;
#use Foo;
tie(*TEST, Foo);
chomp($data = <TEST>, $data);
print join(", ", map { ord($_) } split(//, $data)) . "\n";
chomp($data);
print join(", ", map { ord($_) } split(//, $data)) . "\n";
[download]

and even

package Foo;
sub TIEHANDLE { bless {}, $_[0]}
sub READLINE {return "foobar\n"}

package main;
#use Foo;
tie(*TEST, Foo);
chomp($data ||= <TEST>);
print join(", ", map { ord($_) } split(//, $data)) . "\n";
chomp($data);
print join(", ", map { ord($_) } split(//, $data)) . "\n";
[download]

produce expected output:

102, 111, 111, 98, 97, 114
102, 111, 111, 98, 97, 114
[download]

My intuition says to me that it's not because of implementation of tied filehandles is incomplete, but something with a deeper level of strangeness.
Hmm... I think I'll post this to perl5-porters list.

Courage, the Cowardly Dog.