A number of things that Reese says about the nature of time travel in The Terminator turn out not to be exactly true. There are different ways of viewing this. Personally, I just accept that there is a certain amount of discontinuity between The Terminator and Terminator 2. However, there are other possible interpretations; Reese might be misinformed about the teleportation, or things might be changed by the existence of multiple timelines.*
However you want to interpret it though, the upshot is the same: Some of Reese's statements about the time travel process are shown (in Terminator 2) to be incorrect. Besides the issue of fleshy coatings, Reese avers that the time travel facilities were destroyed, so that no other agents could be sent back in time by either side. Obviously, that claim is not consistent with what happened in the later movies.
Regarding the specific question of how the later terminators were able to pass through time without any apparent coating of living matter, the idea that Reese is simply mistaken might actually be a pretty good bet. Reese is obviously unaware of the existence of shapeshifting terminators, and he is not an expert of the scientific underpinnings of teleportation. The way he understands the situation is that the teleportation will not work without the right kind of coating, which (as far as he knows) limits it to living matter. However, we know, even from the first movie, that "living matter" is not quite the right property, as Kyle makes the journal back through time with his (nonliving) hair and fingernails intact. So whatever physical property that living matter possesses that makes time travel possible might conceivably be mimicked by the more advanced liquid metal terminators (of which, remember, Reese knows nothing). What he says about living matter being required is just a rough approximation—what Reese has been told by the human experts who operated the time travel equipment (who may or may not have a complete understanding of what can be sent back themselves).
*The first film presents a clean example of a close timelike loop, but all subsequent media require a model of time travel in which multiple inconsistent timelines can exist.