With banks, there is another element - they have their own contracts and addenda - check the addenda you signed. See if there is something that says the contract execution date will be when they notify you that your offer is good (even though they haven't signed it yet). I have seen some like that before. If not, then your Realtor needs to tell them to change it.
Great advise by other agents. Seems like there is a misunderstanding on the correct execution date. If you signed on one day and they executed it for the day before, then your agent and broker need to contact the banks agent and correct the date and challenge it. The date of an executed contract is when the last party signs the contract. Your agent and their broker can fight this and if the bank is not cooperating consult an attorney.
Best of luck,
Second, one has a binding contract (assuming all the other elements of a valid contract exist) once all parties have agreed to the terms contained within the document and the last party is notified of acceptance of terms by the other party. The problem is that it becomes a liar's contest as to when the last party was notified of acceptance of the terms.
IF any changes were made to your initial offer, then it doesn't matter what date the sellers signs since they have rejected your offer and countered it with another offer. As such, you have not yet accepted the bank's terms and you don't have a contract...you have a counter-offer.
Consult your realtor and a lawyer. Your realtor should also be able to communicate this lapse of time and work something out with the bank's agent. Request an extension for all the contingencies and closing, if necessary, and get it signed by both parties.
Document, document document the process:
Best of Luck.