I can replicate your results
with Perl 5.8.8 and Tie::File 0.97 and
with Perl 5.10.0 and Tie::File 0.97_02.

sort is optimized to sort in place when the source and destination are the same.

>perl -MO=Concise -e"@a = sort @a" 2>&1 | find "sort"
7           <@> sort lK/INPLACE ->8

>perl -MO=Concise -e"@b = sort @a" 2>&1 | find "sort"
7           <@> sort lK ->8
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I don't know if it's a bug in Tie::File when dealing with sort's optimization or a bug in sort's optimization when dealing with tied arrays, but the bug can be avoided by avoiding the optimization:

@tied_array = map $_, sort { uc($a) cmp uc($b) } @tied_array;
[download]

Update: Better yet,

@tied_array = ((), sort {uc($a) cmp uc($b)} @tied_array);
[download]