Through the power of science!!!
You said "The process that causes the intangibility is based on fictional science and is not of magical or supernatural nature."
If this is true, then that means this phasing is a physical process of some sort, one that a human body is able to generate and maintain.
Since this process is not magical or supernatural in nature, then it must be some natural (non-magical, not supernatural) process that can probably be replicated. Since it is (presumably) a human body producing and sustaining this process, then it must not require a tremendous amount of energy to sustain.
So since this is (probably) a physical process, it is very likely that we could find a way to observe it - specifically the method behind it - beyond simply saying that it's phased now and it wasn't before. And since this process is able to be generated and then sustained by the energy within a human body, it is well within our means power this process with technology rather than biology, if we can just learn how the process works!
Assuming that this power is not unique, that you are able to find someone with this ability who is willing to cooperate, and that you have sufficient funds for this, it would be easy (I'd go as far as to say trivial) to find a physicist or other notable researcher willing to study this ability. It would be even more trivial to then script this scientist or research team (you do get to decide this, after all) to make a breakthrough (they're brilliant!) and gain a significant understanding of this process!
And at that point, you now have both an understanding of the process, and sufficient power to recreate it! All you need then is a little more research and a little bit of hand-waving (no need to actually explain the process), and now you can reproduce this effect yourself!
But how does this let me defend myself?
Well, if you have the understanding and the means to power this phenomenon, then it's not hard to imagine building something able to disrupt this phenomenon as well! After all, your researchers understand this process very well (they're rather enthusiastic about opening a new branch of science), and they've made a number of breakthroughs!
For example, they now know not only how to replicate this process, but also how to disrupt this process! And once they know how to do it, it's only a matter of time before they build something that can do it! They're scientists after all, and one of the fundamental principles of science is verification!
Admittedly, there's no guarantee that this process will be as easy to perform as the original phasing process we observed, so it could be particularly expensive to do so. Still, a little bit of handwaving and this process's resource consumption becomes at least manageable, if not insignificant.
Now if you have the resources to fund the research into this, then you almost certainly have the resources to either patent this technology or otherwise acquire this technology somehow. Even if you don't have those resources (perhaps you are a competitor to the people who did fund this research), there are... other ways to acquire it. But regardless of how it's done, you need that technology if you want to keep yourself safe from people who can phase.
And once you have that technology, all you have to do is deploy it in such a way to keep you and your assets safe from those... phasers?... who would otherwise do you harm! Generate an anti-phasing field around your home! Set up a "honeypot" safe in a sealed room as bait and trap the phaser when they try to break in! Build an anti-phaser into a gun, and briefly activate it whenever it fires a bullet! Doesn't matter! You now have the means to block, trap, and kill a phaser just like you could any other person!
As for how this technology works, what its limitations are, and so on, that's whatever you want it to be. Have fun!