Phase offset and time delay (time offset) are NOT the same and I think this may be a primary source of confusion (Given the OP's other recent posts dealing only with time offset but here the formula used introduces a carrier phase offset). Hopefully the following diagrams help distinguish the two.
No Time or Phase Error
Below is the constellation diagram and eye diagram for the (raised cosine) QPSK waveform in the receiver after the matched filter, with no phase or time offset and showing the decision locations in red:
The eye diagram for the real component of the signal is shown below and should be clear that the imaginary component would look identical:
The blue circles are samples with 4 samples per symbol, one of which is at the ideal sampling location (at sample number 3 and 7 specifically; this eye diagram spans over two symbols).
Next a small time offset (timing error) of about 1/3 of a sample is introduced to show the effect of time offset alone.
With the time offset back to 0, a phase offset of $\pi/10$ is introduced showing it's effect on the constellation and eye diagram.
Phase Offset and Time Offset are two different parameters that each independently need to be corrected (one can exist without the other). Further, phase offset is typically changing with time, which specifically then when changing at a linear rate is a static carrier offset since frequency is the derivative of phase with time, and is corrected with a carrier recovery loop (while time offset is corrected with a timing recovery loop).