I don't understand what you consider "wrong" in the posted simulation waveforms. I don't recognize missing pulses or similar artefacts. Please clarify where exactly you see a problem.
I presume that an asynchronous circuit like this has some timing requirements, e.g. a certain path delay for the reset signal to guarantee a sufficient reset pulse width. Otherwise one of both channels might miss the reset. These prerequisites are not necessarily discussed in the literature suggesting the phase detector. As far as I remember e.g. Razavi only shows a circuit without further comments.
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In addition, there's a circuit discussion in Razavi, Design of Integrated Circuits for Optical Communications, paragraph 8.2.2 Phase/Frequency Detector and Charge Pump. Similarly in Razavi, RF Microelectronics.