I've somehow managed to make it work. I still don't know the exact cause of the problem, but I think there's some kind of setup on the Simulink model that must be done before someone starts to work with the parameter estimation tool.
The reason for that hypothesis is because different from the file used for the parameter estimation of the lithium ion battery on the video I mentioned before, the one I got from the download section seems to be missing some kind of model configuration that wasn't shown on the video, since for example, I had to manually change the solver type, the simulation time isn't the same and there are no inputs configured to the inport of the model, so I can't run the simulation like on the video.
The second reason for the hypothesis is that I've managed to make it work, by putting the battery's circuit model in a copy of a different Simulink model I've downloaded from Matlab, in which I've successfully performed the parameter estimation during previous work.
Does anyone know what am I missing when configuring my model for parameter estimation, so I can avoid the same mistake in the future?