Would it be correct that @$self->{'column'} is trying to dereference $self first ...

My narrative would be that @$self->{'column'} is trying to dereference $self first as an array reference (it's not; it's a blessed hash reference).

... and then access the column key of the dereferenced value?

Once the attempt to dereference a hash ref. as an array fails, that's it: parsing cannot continue. If parsing went on, it would have to deal with an expression equivalent to
    @some_array->{'column'}
that makes no Perlish sense. Looked at another way, even if the proper hash reference dereferencing operator (the % sigil) were used, the expression would still make no sense (update: now; see Update below):
    %$self->{'column'}
is equivalent to
    %some_hash->{'column'}

Update: Well, actually... It dawned on me that a long time ago, in a Perliverse far, far away, this sort of expression did, briefly, enjoy some validity:

Win8 Strawberry 5.8.9.5 (32)  Mon 03/29/2021  3:40:28
C:\@Work\Perl\monks
>perl -Mstrict -Mwarnings -l

my %hash = qw(column vertical  fence horizontal);
print %hash->{'column'};
Using a hash as a reference is deprecated at - line 3.

my @array = qw(column fence);
print @array->[1];
Using an array as a reference is deprecated at - line 6.

my $ar = \@array;
print @$ar->[0];
Using an array as a reference is deprecated at - line 9.

^Z
vertical
fence
column
[download]

(Update: Changed 5.8 example to include array reference; hash reference assumed to work similarly.)

As it was told to me, the history of this syntax is that it began as a bug and was elevated by use into a "feature." As you see, it persisted as late as Perl version 5.8, although even by then it was deprecated. By version 5.30, it was entirely extirpated:

Win8 Strawberry 5.30.3.1 (64)  Mon 03/29/2021  2:54:54
C:\@Work\Perl\monks
>perl

my %hash = qw(column vertical  fence horizontal);
print %hash->{'column'};
Can't use a hash as a reference at - line 3.

Win8 Strawberry 5.30.3.1 (64)  Mon 03/29/2021  2:55:26
C:\@Work\Perl\monks
>perl

my @array = qw(column fence);
print @array->[1];
Can't use an array as a reference at - line 3.
[download]

Of course, something like @$hash_reference has always been verboten.