After being surprised by the output, I realized that this really isn't a namespace issue at all. Rather, it's a compile time/runtime issue.
Both use constant statements are executed at compile time, but the assignment to $x doesn't happen until runtime. When the second use constant is executed, $x is not yet defined, so Second::MULTIPLIER gets the value 2.
At runtime, $x is assigned the value of MULTIPLER in the First package, which is 25, and then multiplied by the value of MULTIPLIER in the Second package, which is 2.
Try this variation, where $x is assigned at compile time:
#!/usr/bin/perl -w
use strict;
package First;
use constant MULTIPLIER => 5*5;
my $x;
BEGIN {$x = MULTIPLIER};
package Second;
use constant MULTIPLIER => defined $x ? First::MULTIPLIER : 2;
print MULTIPLIER * $x, "\n";