Wow, a reasonably toned post regarding placement. I respect that, so I'll help you out:
Soft reset works like this:
[(Previous Season MMR - 1200) / 2] + 1200 = Soft Reset MMR for New Season
People further away from 1200 MMR (both over and under) will receive the most loss/gain. Note this Soft Reset MMR is used for your initial placement match.
Upon beginning a new season, your match results on your MMR changes will be affected by Accelerated Placement. Accelerated Placement multiplies your MMR gain/loss, starting at nearly double and slowly degrading as more games are played. It is not exactly know how many games are affected, but we know that the first 10 games (essentially your placement matches) are definitely effected. Beyond the first 10 games it is just speculation, but I feel that it effects 5-10 games beyond placements.
So your first 15-20 games in ranked have a greater effect on MMR then usual. Remember that it degrades, so your first few games will have a big, huge effect on MMR, with then 15th to 20th games only having a slightly bigger effect on MMR, to finally any game after that will have normal effect.
Now you got to realize the MMR effects themselves vary from game depending on the average team MMR differences. Each of the 5 players on one team will all have different MMR ratings. All 5 players MMR will be added together and divided by 5 to create an average for the team's MMR. Likewise, this will happen for the enemy team. If both team MMR ratings are the same or similar, the change in MMR from a lose or win will be normal. If your teams average MMR is higher, you will gain less MMR from a win and loss more MMR from a lose. Likewise, if your team MMR is lower then the opponents, you will gain more MMR from a win and loss less from a lose. These MMR effects are amplified by the difference in team average MMR, the more the difference the more the effect.
If that wasn't complicated enough, remember the Accelerated Placement above? The MMR change is further effected by the Accelerated Placement (which degrades based of games played).
So ta-da, that's how it works. While a lot of players judge their results solely on wins/loses, you'll see that people often overlook the effects of how much their MMR actually changed based off that win or loss. This could easily vary based off effects of each team's average MMR (which can definitely vary as a soft reset just happened) and how far into Accelerated Placement they are.
Lastly, consider the person's last season MMR. The MMR system is suppose to average itself off over many games played. With the MMR volatility of of the first 20 games, I would say you need at least 50+ games for it to settle out and more accurately reflect your true MMR. Some players never play past the first 10 placement games, or maybe just a few more past that to avoid MMR degradation from inactivity. This could further explain such massive swings in tier and division placement. Their previous season's MMR rating never really stabilized in the first place, so going through the placement process again in this season really swings things all over the place.