How are copyright transfers for a journal article done?
There are very few kinds of contracts that require a full written form and a signature (depends on the legal system, but I think in most places real estate is the common exception). It's just easier to prove the existence of a written contract than an oral agreement if things go to court. 

But in this case there seems to be no need. You said yourself, that the terms in the instructions you are supposed to read before submitting, so you can hardly argue to have missed them. You also cannot really argue that the terms are unreasonable or unexpected, since a copyright transfer of some form is to be expected when publishing.

Legally what happened is that the publisher offers a contract that involves transfer of copyright in case of acceptance and you agreed to that contract by submitting.