the syntax is wrong, what you need is

push @{$aod[$id]},$value;
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@aod[$id] would be a 1 element array slice.
with @{$aod[$id]} you are saying that the scalar in position $id in your outer array, is to be used as a reference to an array. Since push needs to be passed an array, not a reference, you use the dereferencing syntax @{} to give it what it needs.
The first time you push on a particular element the nested array gets auto-vivified, that is automatically created when needed.