Creating an Eye Diagram for QPSK Simulation
Your eye diagrams for the inphase and quadrature baseband signals are perfectly correct. For QPSK with rectangular signals and perfect matched filtering, the inphase and quadrature signals are indeed just BPSK with rectangular signals, and the matched filter outputs can be deduced from, for example, the figure (reproduced below) at the end of this answer of mine.



If you sketch the matched filter output between $T$ and $5T$, overlaying the signal in chunks of length $2T$ centered at $2T$ and $4T$, you will see that the signal is flat at the lower level when two $1$s are transmitted in succession. Similarly, the signal will be flat at the upper level if two $0$'s are transmitted in succession. For transitions between two data bits, the matched filter output crosses over.

As to where the smooth transitions instead of straight ramps come from, if the modulating signal is not a rectangular pulse, or if the matched filter is not quite matched perfectly, the filter output can well be smoothly transitioning from one level to the other. For example, if the BPSK pulse were one cycle of a sinusoid of period $T$, specifically
$$s(t) = \begin{cases}\sin\left(\frac{2\pi t}{T}\right), &amp;0 \leq t &lt; T,\\
0, &amp;\text{otherwise,}\end{cases}$$
then the matched filter output would be a perfect sinusoid of period $T$ between two successive sampling instants if the two data bits were the same, and make a smooth transition from peaking at $nT$ to peaking with opposite polarity at time $(n+1)T$.
See, for example, the figure below.