High-intensity extreme ultraviolet (XUV) pulses from a free-electron laser can be used to create a nanoplasma in clusters. In reference Michiels et al (2020 Phys. Chem. Chem. Phys. 22 7828-34) we investigated the formation of excited states in an XUV-induced nanoplasma in ammonia clusters. In the present article we expand our previous study with a detailed analysis of the nanoplasma evolution and ion kinetics. We use a time-delayed UV laser as probe to ionize excited states of H and H2+< in the XUV-induced plasma. Employing covariance mapping techniques, we show that the correlated emission of protons plays an important role in the plasma dynamics. The time-dependent kinetic energy of the ions created by the probe laser is measured, revealing the charge neutralization of the cluster happens on a sub-picosecond timescale. Furthermore, we observe ro-vibrationally excited molecular hydrogen ions H2+*< being ejected from the clusters. We rationalize our data through a qualitative model of a finite-size non-thermal plasma.