Is this correct use of 'respectively'?

I am accustomed to using the word 'respectively' as follows:

Jack and Jill went to the hill and the pharmacy, respectively.

and this is the way I've always seen it being used. Is it correct to use it in the following way too?

Jack and Jill went to two places. Respectively, these were the hill and the pharmacy.

Solution 1:

Jack and Jill went to two places. Respectively, these were the hill and the pharmacy.

Um... I am a poet, not a gramophile...

I would have said: ~Jack and Jill went to two places, the hill and the pharmacy respectively.

Um- that is clumsy... repeats...

Jack and Jill went to the hill and the pharmacy respectively.

That sounds right.

Solution 2:

Neither of those are ways in which I would use it, nor have seen it used.

Respectively does not mean 'in that order' in quite that sense.

The way it is frequently used is as: 'Jack and Jill were a boy and a girl respectively' - meaning that 'boy and girl' follows the same order as the names, so the first i.e. the boy, is Jack and the second, the girl, is Jill.

Solution 3:

Jack and Jill went to the hill and the pharmacy, respectively.

This parses as the equivalent of

Jack went to the hill.

Jill went the pharmacy.

Whereas this

Jack and Jill went to two places. Respectively, these were the hill and the pharmacy.

Is a somewhat unusual use, and I would assume it meant the same as

Jack and Jill went to the hill.

Jack and Jill went to the pharmacy.

The only case I can think where the construct would be used would be for effect, such as:

Jack and Jill went from bad to worse. Respectively, these were Luton and Watford.