This behavior is documented very clearly:

perldoc -f my
A "my" declares the listed variables to be local
(lexically) to the enclosing block, file, or "eval".
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There no such thing as a "package scope". To do what you want you'd have to use blocks:

$ perl
use strict;
use warnings;

{
  package one;
  my $var = 1;
}

{
  package two;
  my $var = 5;
}

package main;

print "$var\n";
Global symbol "$var" requires explicit package name at - line 16.
Execution of - aborted due to compilation errors.
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Also, FYI warnings and strict are filescoped also if they aren't in a more specific container.