Tosafos explains that the mishna says the vessels are "completed" b'tahara rather than made b'tahara bec. it is not common to watch them until they are close to being finished since at the earlier stages they are not suseptible to tum'ah. The Turei Even understands from Tosafos that even if one would pay attention to watch the vessel from tum'ah from the very early stages of making it, it would still need tevilah for kodesh. The Turei Even argues and says that the primary concern is that saliva of an am ha'aretz landed on the kli while it was being made and was still there upon its completion. Therefore, if one watched it only at the completing of the vessel, this is a valid concern, but if it was watched from the very beginning then there is no concern at all and would not even need tevilah for kodesh. The Turei even would seem to hold that even if one did not watch the kli from teh very beginning, but some time before the actual completion from a time where saliva would have likely dried up, it would not need tevillah for kodesh. The chumra of tevillah for kodesh would only be if attention was first paid upon the actual completion of the kli and not before so there is a likely concern that the saliva that fell on prior to completion did not yet dry up.
Rashi d.h. keilim hanigmarim, comments that "nigmarim" does not mean while they are completed but rather means close to their completion. It seems to me that rashi understands that even if one keeps watch before they are completed, so it is very unlikely that the saliva was still moist on the kli at the time it was completed, we still require tevillah for kodesh. Perhaps Rashi would hold that if it was watched from the very beginning, then it would not need tevillah even for kodesh, but since we only start watching close to the time that it was completed (even if it is likely for the saliva to have already dried up) it would still need tevillah for kodesh.