I would probably ask a lot of questions. It may be that my spouse would see it as casual dating as opposed to a real significant other. Or it may be that the claim was made in error.
I once had someone tell my gf that she saw me making out with another woman. As luck would have it, I was on camera during the time that the friend saw me. My guess is that it was mistaken identity. She finally believed me but she was very suspicious.
But on the other side of the issue, this same gf had started up hidden relationships behind my back and denied them for a very long time. I was too trusting and just took her at her word. Now I am cynical enough to want to at least double check.