First, I agree that technically, Brian Weigand's answer is valid. However, I think there are two other explanations that fit the context better, one of which is simply a refining of Brian's answer.
There is a small statement in the sequence of events that the OP missed (bolded below). Notice the sequence:
- Jesus makes clay, anoints eyes, and commands the blind man to go wash in the pool of Siloam (Jn 9:6-7a).
- The man leaves and does so (Jn 9:7b)
- The man "came back seeing" (Jn 9:7c; NKJV, no textual variants)
- Neighbors react (Jn 9:8-12)
- Neighbors bring him to the Pharisees for initial interrogation (Jn 9:13-17)
- Pharisees call the parents (Jn 9:18-23)
- Pharisees interrogate man again (Jn 9:24-34a)
- Pharisees cast him out (Jn 9:34b)
- Jesus finds him and makes the statements in question (Jn 9:35-38)
Nothing in the text indicates that Jesus removed himself from where he had placed clay on the man, yet verse 7 clearly states the man came back to that place "seeing." So it may well be that Jesus (and his disciples) were among the crowd of people that the man was first beholding when he returned. It was only after this that the neighbors shuttled him off to the Pharisees and thus Jesus had to then go find him after hearing they had cast him out.
Would Jesus have "stood out" if He were still there? Not necessarily. Recall this all happened in what appears to be a place just outside the temple (Jn 8:59 and 9:1), at least within Jerusalem, so the crowd was likely quite large, and seems enough so that Jesus was able to avoid capture. So there was likely a large crowd, and Jesus and his 12 disciples may not have been "noticed" from among a larger crowd by anyone associated with this event (neighbors or otherwise).
If this possibility is correct, it would make Jesus' statement referring to a slightly more remote past event of the man seeing him just after his return from the pool.
Another possibility is that Jesus is referring to the immediate past, but emphasizing the fact that the man who was blind has seen Jesus. The Greek uses the word καί there with another καί, and so the translation "both" for the first use is reasonable as a translation of καί used in such a correlative sense. But a correlative sense for καί can also be rendered "not only ... but also."1
If the latter English rendering is used, it brings out the emphasis that seems implied to be in the verse "not only have you seen him [you who could not see is the implied contrast], but also it is that one [ἐκεῖνος] who is talking with you!" This translation conveys a more intensive idea, similar to "even you have seen him and it is that one who is talking to you" (as καί can give an intensive idea),2 but that intensive is better expressed in a correlative through the "not only ... but also" rendering.
But a question may arise: why the switch from perfect tense to present tense within the statement ("you have seen ... it is that one who is talking")?
It may simply be due to the switch in subject. The first statement is with the former blind man as subject, the latter with Jesus, though referring to himself as a third person "that one," or the "he" that was the object of the first statement of who had been seen.
But there also is a literary and theological reason in the context. The emphasis in Jesus's statement is on the man having already received his sight, but now was receiving the revelation of the specific individual who performed the miracle, that being the person presently talking to him. This phrasing sets up a reverse contrast with what follows of the Pharisees who already knew the specific individual who worked the miracle, but were yet presently "blind" to His work (v.39-41).
Either concept provides a reasonable explanation for Christ's use of language. He is either playing off the fact that the man had already seen him (but did not know it) after his return from the pool or the fact that the man could now see him (for he had been during their short discussion), emphasizing the miracle (and thus Jesus being who He said He was) and this man seeing that miracle for what it demonstrated, that Jesus was a man from God.
1 William Arndt, Frederick W. Danker, and Walter Bauer, A Greek-English Lexicon of the New Testament and Other Early Christian Literature (Chicago: University of Chicago Press, 2000), s.v. καί 1.f.
2 Ibid., 2.b.