Transfer of copyright is not part of the submission process, it follows from acceptance and is (or should be) a prerequisite for publication. Prior to the publication agreement, there is typically a somewhat vague commitment where the author "promises" that the article has not been published elsewhere and is not under consideration for publication elsewhere, but these rules are not as clearly expressed as being contractual in nature, and in the case of a skeezie journal a clueless author may not have been informed of this promise.
It is relatively rare for a journal to accept and publish a paper without an actual license or transfer of copyright from the author. In lieu of an explicit agreement, the publisher can at least rely on an implicit license, that is, simple permission to publish. This is not an exclusive license or a transfer of copyright. If there is no explicit written agreement, the first publisher will not be able to sue anybody. If the second publisher likewise does not get a written agreement signed, that publisher also cannot sue anybody.
If there is a written agreement (with the first publisher, you can extend this to the second publisher in obvious ways), it will most likely but not necessarily address certain copyright formalities: what the author gives (permission to publish, vs. complete transfer of copyright), and if the agreement is to publish, it should address the durability and exclusivity of the license. The agreement should also include a clause indemnifying the publisher, saying that "If we get sued because of your actions, you must...." (then some clause about the author having to take responsibility). There is, or should be, a clause that avows that the author has the right to make all of these promises.
If the agreement with publisher 1 is an exclusive perpetual license, or one with a long period, the author will have breached the agreement in (somewhat) later submitting the paper to another journal, and the breach arises when the second journal also publishes the article. The second journal could then be sued for copyright infringement, and if their contract includes an indemnification clause and the relevant author's representation, the second journal can force the author to bear the legal burden. If the initial agreement was non-exclusive, then the agreement with publisher 1 has not been breached. But publisher 2 might have a direct case against the author, if the agreement with publisher 2 includes language that is incompatible with the publisher 1 agreement. So if publisher 2 wants complete transfer of copyright, they will have to work out an exception for prior versions in their agreement.
Publisher 2 may not be willing to make such an exception. If not, and if the author does not make publisher 2 aware of the issue, then publisher 2 might sue the author for breaching the agreement. The author might also negotiate with publisher 1 to terminate the first agreement: however, even that might be insufficient w.r.t. breach of the agreement with publisher 2.
So: if there is a written agreement, read the agreement carefully, and think about whether you are making a false statement, such as that you have the right to transfer copyright to the publisher. Your earlier agreement may have taken away that right.