When opening up a relationship, you can wrangle out the details in any fashion you see fit. If that involves restrictions on where to meet people or veto power over potential partners and so on, then that's what it involves. There's no requirement to be binary--everything goes or nothing goes--about your relationships! It's only going to work if everybody can operate with some degree of comfort and security.
As for the man who asked you out, well, why haven't you explained to him what's going on? He deserves the same sort of openness as your partner. If there is a potential relationship there, beginning it by not communicating what's happening is not a good start.