When you make an offer to the other party, the other party may be able to give you a response during your scheduled mediation, or they may to have a follow-up mediation at a later date to think about your offer. It is up to the other party to decide if they accept or decline your offer.
Likewise, when a party makes an offer to you in mediation, it is up to you to decide if you accept or decline their offer. If their offer works for you, say so. Then parties can talk more about the specifics of the agreement. If their offer doesn't work for you, it is helpful if you explain the reason why the offer doesn't work for you. If you would like more time to evaluate their offer, consider asking if the other party is willing to do a follow-up mediation.
Mediation doesn't have to end if the first offer is not accepted. Either party can respond to an offer with a counteroffer.
Trading offers back and forth in a respectful manner may help you eventually reach agreement. If it doesn't, then hopefully each of you will walk away with a better understanding of the disagreement.