Both, in sequence: First general, then specific

Firstly, in Hermeneutics, consider context. Start at the beginning of the pericope in v12.

John 13:12-14 (NASB)

12 Then, when He had washed their feet, and taken His garments and reclined at the table again, He said to them, “Do you know what I have done for you? 13 You call Me ‘Teacher’ and ‘Lord’; and you are correct, for so I am. 14 So if I, the Lord and the Teacher, washed your feet, you also ought to wash one another’s feet.

...Here, Jesus explains that him washing their feet his his role as "Teacher" and "Lord".

Feet washing was partly a servant's role, so we should consider other teaching from Jesus about servanthood. Here is a very good and direct example of Jesus's teaching on that...

Mark 9:35 (NASB)

35 And sitting down, He called the twelve and *said to them, “If anyone wants to be first, he shall be last of all and servant of all.”

Therefore, being the "Master" means being a servant of all.

One other major part of this passage is that this is the Last Supper; Jesus will be crucified the next day. Later, in this same Last Supper meeting in ch15, Jesus mentions the master-servant hierarchy again, explaining in more detail...

John 15:20 (NASB)

20 Remember the word that I said to you: ‘A servant is not greater than his master.’ If they persecuted me, they will also persecute you. If they kept my word, they will also keep yours.

John 15:20 may actually be a direct answer to your Question. But, a Hermeneutics Answer compels us to look at why.

Jesus makes a statement in ch13, then later in the same discussion explains it in ch15. He also did this with his parables (Mt 13, Lk 8).

So, Jesus himself says that he is referring to two things:

1. The disciples will also be persecuted by dissidents.
2. The disciples will also be respected by followers.

Consider a few things about these passages:

• In Mark, Jesus explains the need for leaders to have servant hearts and actions.
• John had already given the nod to Mark's account of Jesus' life in the Early Church; John's Gospel was written after, with John being well aware of what the Church was reading from Mark. So, we must read John as if the ideas of Matthew, Mark, and Luke were agreed to by John because they indeed were.
• Don't confuse Mark as teaching that a servant and master are one-in-the-same, but that a true master is "one who serves", probably serving his own servants most of all.
• Based on John's idea of a servant not being greater than a master, we would conclude that "one is not greater than the one who serves", but that is for accurate understanding; anymore would rabbit trail.
• Jesus is not saying that they are his teachers nor his lords nor masters.
• In John, Jesus is telling them that they, as his "students" or with him as the teacher, they will not receive special privilege or exception from what Jesus must do.

To your multiple-choice question: general or specific? It is first general, explained as a principle in ch13, then applied specifically to the disciples in ch15. So, the answer is both, in sequence: first general, then specific.