They have three months to figure out which one to support. When each miner mines a bitcoin block they get to increment or decrement the timelock on a withdrawal attempt. So they don't have to talk to one another, just decide individually what they want to happen, and then the number will go up or down based on the action that each miner performs. If, without coordination, precisely 50% of miners + 1 increment it every time they mine a block, it will very gradually climb toward the height when the withdrawal goes through. If not, it will gradually recede back to it's initial value, allowing the rightful owner to get ahead.
I'm also simplifying a bit, you can read https://bips.xyz/300 for the full details.
Must 51% of miners be able to co-ordinate in order for BIP300 to be safe? Because one of the beauties of bitcoin is miners dont have to coordinate in order for it to be safe. And by the time miners have coordinates to increaes the timevalue thing, will it be too late?