The personal phone call policy for each company is different, but most companies I know about have fairly broad latitude given to managers. If the company has a union, they'll have something to say on this topic also, but it is possible that it'll be said in the company's policy.
When you have a family, it's important to find out the company policy and your boss' policy. It may be helpful to communicate your situation at home to your boss, but it's best to do that when they're not upset. It's always a good idea to track exactly how much time you're spending on personal calls. If your employer were lax, you maybe could get away with just noting how long each call was and keeping track mentally. But this guy isn't, so I'd recommend recording a start and stop time for each personal call you get or make at work.
That having been said, that's just useful for next time. You have this time to worry about. But I don't think we have enough information to do that, and I'm not just talking The Workplace SE, but you, too.
Assuming your new boss is not new to the company, there are people around who know more about him and his history with employees taking personal phone calls. Behavior like this doesn't just come out of nowhere. As opportunity permits in the course of your job, or while on breaks, talk with people and ask them about it. As you get more of an understanding of what's gone on before between him and the people who report to him, you may get a better understanding of either how to convince him that you're not a problem, how to not be what he considers a problem, or how urgently you need to find a new job.
That having been said, it would be a really good idea to keep personal calls at work to a minimum until you have a better idea of what the exact rules are. As Philip Kendall said, when you really need to take a personal phone call at work, be quiet and professional about it, and keep it as short as feasible.
One thing I have found with new bosses who seem initially to be a major problem is that they're people too, and they have their own concerns and reasons for them. Sometimes talking with them about their concerns can lead to finding a path that will work for both of you. But don't try to force a conversation. That's generally a good idea at work with people who don't work for you, but it goes double with anyone in your management chain.
Maybe he'd appreciate it if you put in extra time to compensate for any time you spent on the phone. Of course, it's a good idea to determine if that is even possible before suggesting it to him. When I worked in a union shop with a physical punch clock, suggesting such a thing would immediately get people on the union steward's bad list, in addition to annoying whomever they suggested it to. At another employer, making that suggestion and then sticking to it was an effective way to get the boss to ease up on me.