How was the 95% miner adoption threshold determined?
New softforks are activated using BIP 9 (versionbits), which specifies the threshold requirements. The 95% threshold is inherited from the old BIP 34 (supermajority) softfork activation method.

A softfork with greater than 50% hashing power should always become the dominant chain because the upgraded miners will create a harder difficulty chain, and the non-upgraded nodes will be pulled onto that chain because it's still valid for them (soft-forks are backwards compatible). However, any non-upgraded miners may create blocks which are invalid under the new rules. Those blocks will be orphaned off the new chain. The lower the miner adoption rate, the higher this new orphan rate will be.

In reality, as soon as the threshold has been reached and the softfork is locked in, almost all miners will upgrade to the new rules.

The 95% rate is a very conservative threshold to ensure that there is widespread consensus for the new change.


  miners who have not activated SegWit, will still confirm SegWit transactions 


This isn't true. If a miner hasn't activated SegWit, then it can't include SegWit transactions in its block (to include a SegWit transaction, it would need to include the witness data and commit to the merkle root of the witnesses in the coinbase transaction). BIP 141 documents all the consensus rule changes for SegWit.