Briefly: If the overall perceived brightness is the same or lower, and the screen looks less blue to you, then yes, the program reduced the amount of blue light coming off of the screen.
So, all you can do is reduce the proportion of blue, relative to red and green.
If the overall brightness looks the same to you, then the program also increased red and/or green to keep the brightness the same.
Just increasing red and green would have had the "less blue" effect but would also have increased the apparent overall brightness. (So your iris would likely close down, so you would be getting less blue light on your retina.)
A "hardware filter" (that is, a piece of colored plastic over the screen) of course can't do anything but throw some of the light away. So all three channels will be dimmer than they were. By dimming the blue more than the others the filter makes the screen appear more yellowish (and also dimmer overall).
A comment suggested that perhaps the program could be reducing the amount of "bad blue" light, replacing it with "less-bad blue". I'm sorry, but that isn't possible for a program, nor for an add-on filter.
The signals to a computer monitor only let us pick brightness levels for three different "primary" colors: red, green, blue. There is no way to tell a monitor "use this blue instead of that other blue". Whatever "blue" the monitor is built to produce, that's what you get. (Same for green and red, of course.)
From an LED-backlit monitor, the situation is even more strict, because all of the "blue" coming from the LEDs is in one fairly narrow range of wavelengths. (In fact, it's nearly monochromatic - only lasers and special laboratory light sources have narrower spectra!) That's what "white" LEDs produce: A big narrow spike of blue from the blue LED and then a broad swath from the phosphor covering green and red.
With a CFL-backlit monitor the "blue" is in a wider swath and with far less output in the shorter wavelengths than LEDs. (See the diagram below.) But the filters in the monitor still just select a particular part of that swath for "blue". The LCD panel engineers pick the color filters for best color rendering, and this choice is "baked in" to the monitor design. There is no signal in the world you can send the monitor to tell it "change the wavelengths you're using for blue to this other part of the blue range."
However, the shorter the blue wavelength, the more eyestrain, and it may be the case that CFL-backlit panels will produce less eyestrain than LED-backlit, because the CFL's blue has less power at the shorter wavelengths. Some monitor makers are sticking to CFL for their higher-priced "pro" models because of better color accuracy (but with higher cost, greater weight and bulk, and more power consumption).
This diagram shows the spectra of two different types of LED backlights, and of two different types of CFLs:
(diagram from this page by Eizo, a monitor manufacturer)
So, no. No program can cause the monitor to change from worse blue to better blue; the monitor has no other "blue" available to change to.
And even if it had, we'd still have some of the same problem, because all "blue" light is fairly similar in terms of eyestrain. It happens because all of our cone cells for blue light (regardless of "which blue") are rather far away from the center of vision. But the cones that respond to red and green are in the center.
Because of that, our eyes have a really bad case of chromatic aberration when it comes to blue. In other words, we literally can't focus correctly on both blue detail and anything else. Our eyes' lenses have to pick one or the other. But our brain keeps trying to bring everything into focus, and that tires the muscles that shape our lenses.
This by the way is why headlights with a bluish tint look overly bright: We can't focus on the blue component well, and our brain interprets the resulting blur as glare. So we want to look away from it.
What about those Benq monitors?
All of the above was written with regard to the OQ, which had to do with programs like f.Lux added to the system to change the color balance. But what about the claims made by Benq for their monitors (as quoted by @miroxlav)? Well...
First - I'm afraid that the spectra depicted by Benq's diagrams are what we on the engineering side of the house call "cartoons". There is no light source used for monitor backlights that produces such broad, evenly-distributed spectra with no peaks! If they'd published a true spectral intensity graph, with actual irradiance levels shown on the Y-axis, we'd have something more definite to talk about.
So what are they doing? What could they be doing that's consistent with their claims (ignoring the misleading spectra depiction)? Likely they're using a CFL, with the addition of a color filter to block the shorter-wavelength blue.
Another possibility would be "white" LEDs that use a longer-wavelength blue LED... but those would be quite inefficient. And yet a third, very expensive possibility would be true RGB LEDs with the "blue" chosen for a longer wavelength.
But any of those options leave an open question as to color rendition. The better color rendition of CFLs over LEDs is partly because their light does include those shorter-wavelength blues (just not in a narrow peak). To reproduce those blues (indigo and violet) the monitor just has to emit those colors. There isn't any other way to get our eyes to perceive them. Mixing red and blue gives "purple", or more correctly "magenta", which is often used as a substitute for violet. But it doesn't look the same as a true violet (i.e. the shortest wavelength in the "blue" range).