It's not explicitly stated, but the most likely answer is that the the character had a flesh covering for their initial trip back in time, then shed it when it was no longer useful. We could make the same assumption about the T-1000s. A living flesh covering isn't particularly useful when you can shapeshift at will, and don't plan on time travelling.
Since John Connor's exposure to the incomplete time machine at the end of the film was unplanned, and he was shapeshifting like crazy up into that point, it stands to reason that any flesh cover he may have previously had would've been dropped or shredded.
Since John Connor was human prior to his transformation, it's possible that Skynet just didn't fully convert the outer layer of his flesh, since it was planning on sending him back in time immediately. Then, it would've been shredded as soon as he shapeshifted some clothing upon arriving in the past.
Those are just my guesses based on the available evidence. It's also possible that the incomplete nature of that particular time machine had something to do with it.