When you moved it did you notice if the nurse root was still there? I would think your tree peony would be on it's own roots completely after 4 years. I bet you're seeing new tree peony growth now that it's been in its new spot for a full year.
Tree peonies can do weird things. I have 3 that are the same, 2 in back yard and 1 in front. The 2 in the back behaved exactly as they always have last year but I thought I'd lost the one in front. It didn't start growing at the same time as the 2 in back, had in previous years. It had a lot more growth from the ground than the other 2 and almost no growth from the woody branches. I ended up cutting out most of the old growth from that one but it managed to put out several blooms from the new growth and now I have lots of 1 year of woody stems on it. Still no clue as to why it behaved as it did.