I am curious, do you feel you need to say hi to them before they have met your husband for say....coffee? Do you feel the need to talk to them if the relationship is going to stay at a level of online flirting? I can understand if your husband is likely to form an emotional connection with somebody before they ever meet, the desire to say hi to them earlier. I can also understand if the other person doesn't identify as poly, it could be more vital to let them know you are present and aware of what is happening, to avoid misunderstandings.
I certainly imagine it would feel awkward to have a potential metamour want to talk to me before I have even had much conversation with the person I was interested in if the interaction was online only. However if it is going to happen, just keeping it to "my wife says hi!" if she comes in the room while we are talking, or walking by and waving during a hypothetical webcam chat would not make me uncomfortable. If it's important you say hi when your husband tells you about an interest, you could ask him to to schedule the next talk for a time you are available to do that if it's causing anxiety. However I do think if you need more than that (ie emailing the person) during their preliminary "getting to know you" phase, it is probably important you really work on your motivations, as a lot of people would find that awkward.
Throwing a random idea out there, that maybe has a bit of a chance to combat anxiety - any possibility your husband is willing to commit to asking a person he is flirting with out for coffee within 2-3 weeks of starting to talk to them? He'd get to meet them and see if there was actual interest, and you wouldn't have to wonder if this ongoing flirting was going to lead anywhere and stress out about it. Just something I'd noodle over trying if I was anxious and in your situation. At the very least your husband can figure out if he is interested in pursuing a person or just flirting with them if he finds he doesn't have a desire to take it beyond online.
Happiness will never come to those who fail to appreciate what they already have.