This strikes me as a rather nit-picky detail, but I can understand why you would want this behavior. The question is: is it only this sort of statement that is making trouble for you? If so, how bad is it just to edit perltidy's output yourself to fix these cases? Or, if there are a lot of these, and they all end up following the same basic pattern, why not try an ad-hoc filter on the perltidy output -- something like:

s/^(\s*)(my\s+[^\s=]+)\s*(=[^;]+)$/$1$2\n$1    $3/;
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For lines that look like  my $var = ... and lack a semi-colon on the rhs, this substitution will put any indentation that precedes "my", plus another four spaces of indentation, at the beginning of a new line that holds just the "= ..." portion.