Publication process in a journal
Journals have deadlines for publication. Everything that will go into issue X needs to be ready by date Y. If you meet their deadlines you increase your chances for early publication, otherwise you may be put off. 

However another problem is that while the reviewing is "normal" the editorial process of choosing papers for issue X also comes in to play. The other language of the publisher's reply might imply conditional acceptance if returned by the date given. After that, unless you already have acceptance, it might become more tenuous. 

Basically, what they are saying is "We have constraints here. Please help us meet them." It would be good, if not essential, to honor that.