As soon as a transaction is sent from an address with an insufficient balance, that's when the split will occur.
This is a profound misunderstanding of how Bitcoin works, there are no 'balances' in the system.
And unmodified non-segwit miners will not initiate a split under any condition.
Any rollout of segwit must include majority hash power
No, that is one sufficient condition, it can instead include basically all of the users (in particular, economically significant users). Either are sufficient alone. The users define what are the miners and if the user define mining to include segwit, it does... from their perspective it is impossible to violate the rules, and any miner that tries just stops existing-- just as litecoin miners do not exist as far as Bitcoin users (and their nodes) are concerned today.