If the miners hard fork that means they create blocks that are invalid according to the previous rules. So exchanges and users with a node will just reject blocks from these miners, unless they also change the rules enforced by their own node. They will naturally follow the non-forked chain. They will be stuck there if all the miners apply the hard fork rules, but it requires only a few miners to keep the old chain alive.
The agents decide which chain to follow be choosing what rules their node applies. They have to actively change their client software to follow a hard fork. Of course users who don't run their own node and rely only on exchanges depend on the decision made by their exchange. But in a controversial fork most exchanges would probably not pick side and handle both chains as two different coins. They would still have to somewhat pick a side by choosing the name of the coins though.
What's also interesting is that anyone owning coins before the fork will have the same amount of coins on both chains. That happened in 2017 and the price almost instantaneously split to about 90 % of the previous value to the previous chain, and 10 % to the new chain. Users rejecting the fork could just sell their Bitcoin Cash for Bitcoin and return to their initial value in Bitcoin.
The agents decide which chain to follow be choosing what rules their node applies. They have to actively change their client software to follow a hard fork. Of course users who don't run their own node and rely only on exchanges depend on the decision made by their exchange. But in a controversial fork most exchanges would probably not pick side and handle both chains as two different coins. They would still have to somewhat pick a side by choosing the name of the coins though.
What's also interesting is that anyone owning coins before the fork will have the same amount of coins on both chains. That happened in 2017 and the price almost instantaneously split to about 90 % of the previous value to the previous chain, and 10 % to the new chain. Users rejecting the fork could just sell their Bitcoin Cash for Bitcoin and return to their initial value in Bitcoin.