After creating a blurred mask to cover a face, I had to track it manually. I tracked both path and position values individually. However, when moving forward in the timeline, the mask shifts to the new position, affecting previous sections too.

With the new masking tool, you need to switch the masking mode from Clip to Frame mode to make manual adjustments over time. Hopefully this helps:
https://helpx.adobe.com/premiere/desktop/add-video-effects/create-masks-and-composites/adjust-masks-at-the-clip-or-frame-level.html

Hi ​@attiliovalli 

Welcome to the Premiere Pro Forum community. Thank you for taking the time to report a problem. It would help us if you could use the link " How to Report a Problem," which provides steps to provide more information that can help us identify the issue. Which version of Premiere are you currently using, and have you tried the new object masking tool for simpler masks? When you step into that mask, are you seeing keyframes? If you used the track forward and track backward options before you manually entered your keyframes, make sure to reset all keyframes, or drop the clip back in clean before adding your keyframes. 

Here to help.  

Ian