The interstimulus interval (ISI) for vision is much longer than most flicker rates or frame intervals in displays and projectors. However flicker can be perceived through temporal aliasing. For lighting, even simple motion in the scene can reveal flicker. Waving your spread fingers in front of your eyes is a sure way to detect flicker.
What you're describing is likely saccadic masking, where the brain suppresses visual input during eye movements. It "freezes" perception just before a saccade and masks the blur, extending the perception of a "frame" up to the point in time of the sharp onset of masking. That's how you get a still of a partially illuminated frame instead of the blended together colors.
I’m no expert in this, but if you're curious, check out the Wikipedia pages on interstimulus interval, saccadic masking, chronostasis, and related research.
Not only DLP. Some laser projectors use a color wheel to get the same effect; other laser projectors use multiple lasers, but pulse the colors individually and you get a similar effect; probably there are some laser projectors that do all colors simultaneously too, just as there are some DLP projectors with 3 DLP surfaces and prisms/etc to split and combine the light. My laser projector does the pulsing, I find it slightly less distracting than I remember color wheels being, but it's very similar; thankfully the family has gotten used to it; I only notice it on content that encourages a lot of fast eye movement.
Scanning displays like a laser projector or a CRT will flash any individual spot but the illumination is almost continuous, so people have less issues with them.
I'm talking about laser illuminated panel projectors used for viewing film or video content, not scanning lasers used for light shows. Scanning a laser beam is a lot more difficult than scanning an electron beam, so rasterised displays from a scanning laser are limited compared to CRTs.
I believe the colour wheels now spin twice as fast which may reduce the effect somewhat. But for me it's not a very nice effect which is why I use a 3 chip projector. Unfortunately 3 chip DLP is prohibitively expensive (cinemas use them), but JVC DLA projectors are good. Although it looks like the newer 4K models are also prohibitively expensive :/
LCDs have typically been considered inferior for home cinema usage. The only advantage of them is the price and that they have no colour wheel. DLA is a sort of middle ground that is technically an LCD but works more like DLP. None of this matters if your room isn't set up right or you're projecting in a not completely dark room, though.
I know. I was just pointing out that flicker doesn't affect me, for which I'm glad. I was a bit concerned before I bought it, due to the complaints about the flicker.