So I found more information about this topic (since I am going thru this right now and also looking for answers).
There is a research called "Clinical assessment of peripheral nerve injuries; Tinel's test." (HENDERSON WR., 1948), that followed many nerve injuries.

To summarize it, after an injury where the nerve structure was left intact but the axons were damaged enough to break their continuity (the least severe axonotmesis injury), it takes 1-2 months until the tinel sign starts to progress. After that, it can to take up to 6 months from injury until the "tail" of the sign will start to fade completely. (the length of the tinel 'wave' can be up to 6-12 inches)
In some cases there may be incomplete recovery, and the wave will be longer because of some fibres that struggled to grow but managed to do it later, and after it will be gone, slight sensitivity may stay in the injury site because of the fibres that failed to grow and are permanently stucked.

In more severe injury to the nerve, where the structure was damaged but there is partial recovery, the whole nerve may stay sensitive because fibres are continuously leaving the injury site (in delay).