Same thing happened to my friend.
He went from Legend (2) to Legend (5) and then Ancient (0) in quick succession.
If I am not mistaken, it is likely due to your hidden MMR (i.e. the MMR that you play at, as opposed to just your medal-based rank). It could be that by the old system, your MMR was higher than your current ranks implied MMR, and so your medal rank will increase to match to it.
Taking the example of my friend, his old MMR was 4K, but legend (2) is about 3.5, so after a few games, it jumped to Legend (5) (approx 3.9-4k MMR) and then Ancient (0) (4+K MMR)
You can actually check it out in the stats page on your dota profile in the top right hand corner. It will show your actual MMR on it.
This is actually over my mind. I was 4.7 k before calibration and got Legend 5 xd and 3900 mmr after calibration(now Im like 2-3 wins from Ancient 4). At the same time my m8 who didint play for months got Ancient 2 with 4100 mmr.
On my smurf with ~4k hidden mmr I tried my best to actually get the lowest badge possible. I lost all of my calibration matches with terrible stats playing mostly afk pudge or Io and got Ancient 2.
From what Ive noticed, everytime I picked a high skill cap hero like Io or Shadow Deamon or Beastmaster, next game I got higher rank despite terrible performance.
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Guys this is so weird like ive been reading articles about this and why this is happening to me right now. Cause I feel that I am much better before than now but still I rank up like a beast idk why lol. someone tell me pls what is happening. Thanks in advance