[Arizhel]

>Tell him/her exactly how much time you give them (3 month is a okayisch thing) to improve on it or you will leave based on that issue.

This seems like pretty terrible advice. You seem to be assuming that the OP is independently wealthy and doesn't really need to work for a living, and can go for many months without a new job. If he were to follow your advice, what makes you think he can just walk out at that time and have a new job that week? He's moved to a new city, which most likely isn't some giant tech city, so it'll take him time to apply for, interview, and secure a new job. If he's allowing the old employer time to meet his conditions, then he cannot ethically start this process until they don't, and either fire him outright (because they don't like being given an ultimatum) or simply don't bother to change and start secretly looking for his replacement. Even if he decided to act unethically, accepting a job offer and then backing out is a good way to get on a company's black-list, and in a smaller city that means you now have one important employer that you can never work for again, and if they share this info with other local employers you're really screwed.

The only rational way to handle this is to make a decision based on the current information.