Can I use Mike, the Dungeon Master to save one of my creatures from a board wipe?

I have a strong feeling that I accidentally cheated last night in my game of commander, I had Mike and Mind Flayer on the field, as well as others. My opponent cast a card that gave all creatures -3,-3. My entire board was gone as well as his, with the exception of one of his creatures. In response, I used Mike's ability to target my Mind Flayer and the board wipe resolved. I returned the Flayer and targeted his remaining creature with it. I had tried to look it up using several resources, but the AI responses were all over the place, and anything else I found on the interaction pretty much said I could do that. Was I able to use his ability to return the Flayer to my battlefield, even if I activated it in response to the board wipe, while they were on the field?