I know I have another girl so it's not the same, but two dogs adjusting is a pretty universal process. For us, we had to keep Maggie and Franklin separated for two weeks. Just to give Maggie time to adjust to the noises, smells, and people. Not to mention they attacked each other any chance they got. After that, they tolerated each other but it took a month or so before they LIKED each other. Give it time. They are both experiencing major changes and they need time to adjust. Every dog is different, it could take days, weeks, or months.
It sounds like you're doing a wonderful job and have done your research. Having them both neutered will help you a LOT, and introducing them on neutral ground was perfect! My advice: they will probably fight a couple of times or so. It may seem violent, but they are just working out who is dominant. Unless you think they are seriously going to hurt each other, don't interfere. Your presence will only make it worse and more confusing for them. Dogs are pack animals and they need to sort out their place in the pack. Eventually, a leader will be established. If that leader happens to be your new rescue, you have to accept that and go with it. YOU are the alpha, but then there is the dominant dog, and everyone else. So YOU eat first and make the rules, but then the dominant dog also eats first, gets first pick of toys, sleeping spots, things like that. It sounds cruel to the submissive dog, but dogs really are more comfortable when they know their place. It is less stressful for them.
Good luck!
