No, they can't simply tell things apart. How should they?
On the air, the transmitted QAM-based signal adds up with the BPSK signal, and even in the exact symbol times, you get numbers with real and imaginary part.
Also, you forget that signals still are pulse shaped; a sensible pulse shaper can have a complex part when going from one BPSK symbol to the other.
What you describe has nothing to do with how MIMO works! MIMO works because for uncorrelated channels, you can find a matrix decomposition of your $\mathbb C^{N_{TX}\times N_{RX}}$ (flat channel case) matrix, not because the signals are different. With that matrix decomposition, you can find "separable" channels, even though the signals add up "on the air" and you just receive a mishmash of all TX signals at each RX antenna (though the amount of the TX signals in that mishmash has to be different for each RX antenna).
Because Zeyad_Zeyad introduces SM but doesn't agree on whether in a MIMO channel, signals from different antennas sum in the air:
The typical MIMO channel is modeled like this:
With each RX antenna seeing a linear combination of all TX signals; hence, the representation as channel matrix $\mathbf H$
$$\mathbf H=\begin{pmatrix}
h_{11} & h_{12} & h_{13}\\
h_{21} & h_{22} & h_{23}\\
h_{31} & h_{32} & h_{33}
\end{pmatrix}$$
so that you can get the first receive signal as the first entry, the second as the second entry, … of
$$\vec r =\mathbf H \vec t\text,$$
where $\vec t$ is the transmit signal vector (i.e. the first entry is the symbol at TX antenna 1, the second at TX antenna 2 …).
As you can see, if say $t_1$ is real but $t_2$ or $t_3$ have an imaginary part, $r_1$ can very well be complex.
So, as you can see, for MIMO to work, you don't need the signals to have different characteristics – you need the channel coefficients $h_{i,j}$ to be independent enough!
Please allow me a personal note from the perspective of someone who helps students survive exams in "Digital Communications Basics" courses at university, @Eng. Badr:
In your previous questions, you were wildly jumping from extremely involved topics like FBMC to more entry-level topics like CDMA then down to the very, very basic of QAM vs PSK (which you had a great misunderstanding about!). Now you're back to a topic that is relatively complex (MIMO) and requires solid understanding of the things like constellations.
You sound like a student who's either preparing for an exam for which they are missing the basic course, or like someone doing a thesis on a topic where they have to acquire basic knowledge by themselves. In either case, jumping into topics, asking a single question, and then jumping to the next topic will not enable you to understand much, and cost very much of your time, without enabling you to do your own deductions. Especially in the thesis case, that's a hazard, because at some point, someone will point at a blaring mistake in what you're doing and say "ok, every person who works on {topic} should know that this can't work, it's really basic".
So, do yourself the favor of getting a digital communications textbook that takes you from the basics of complex baseband over constellations, pulse shaping, a tiny bit of channel coding, over to multi-access schemes like FDMA and CDMA and finally MIMO. I promise that in the medium run, reading that book from start to finish will save you time and effort and, if my hypothesis on the situation you're in is right, will definitely improve the grade you'll be getting.
