In vivo range monitoring techniques are necessary in order to fully take advantage of the high dose gradients deliverable in hadrontherapy treatments. Positron emission tomography (PET) scanners can be used to monitor beam-induced activation in tissues and hence measure the range. The INSIDE (Innovative Solutions for In-beam DosimEtry in Hadrontherapy) in-beam PET scanner, installed at the Italian National Center of Oncological Hadrontherapy (CNAO, Pavia, Italy) synchrotron facility, has already been successfully tested in vivo during a proton therapy treatment. We discuss here the system performance evaluation with carbon ion beams, in view of future in vivo tests. The work is focused on the analysis of activity images obtained with therapeutic treatments delivered to polymethyl methacrylate (PMMA) phantoms, as well as on the test of an innovative and robust Monte Carlo simulation technique for the production of reliable prior activity maps. Images are reconstructed using different integration intervals, so as to monitor the activity evolution during and after the treatment. Three procedures to compare activity images are presented, namely Pearson correlation coefficient, Beam's eye view and overall view. Images of repeated irradiations of the same treatments are compared to assess the integration time necessary to provide reproducible images. The range agreement between simulated and experimental images is also evaluated, so as to validate the simulation capability to provide sound prior information. The results indicate that at treatment end, or at most 20 s afterwards, the range measurement is reliable within 1-2 mm, when comparing both different experimental sessions and data with simulations. In conclusion, this work shows that the INSIDE in-beam PET scanner performance is promising towards its in vivo test with carbon ions.