Jesus said this in the Gospels
First mention: In good hermeneutics, especially from Jewish authors, it is vital that we look to previous times that terms and phrases were used, especially by the same character or author. (This does not encompass the full meaning, but it certainly sets the foundation on which later meanings are built.)
Remember, Jesus himself indeed uses identical words like this on two occasions before: in a parable and in a leadership lesson.
Parable of the harvesters and master
From the parable of Matthew 20:1-16 (NASB, emphasis added)
...13 But he answered and said to one of them, ‘Friend, I am doing you no wrong; did you not agree with me for a denarius? 14 Take what is yours and go, but I wish to give to this last man the same as to you. 15 Is it not lawful for me to do what I wish with what is my own? Or is your eye envious because I am generous?’ 16 So the last shall be first, and the first last.
Here, Jesus speaks as the landowner who has the authority to give whatever reward he deems appropriate. It introduces the idea of laborers who started working at different times in the day, both early and late.
In context, Jesus statement in Revelation 1 likely means that he was laboring both early in the day and late in the day. And, in that story, only the landowner was there all day long; Jesus is that landowner according to Revelation 1.
We should also cross-reference this with other sowing-harvesting speech from Jesus, albeit John the same author of Revelation...
John 4:37 (NASB)
For in this case the saying is true, ‘One sows and another reaps.’
With first and last in the context of harvesting, Jesus is claiming to do both. (Harvesting is also a theme seen in Revelation 14:14-20.)
Mark 9:33-35 (NASB, emphasis added)
33 They came to Capernaum; and when He was in the house, He began to question them, “What were you discussing on the way?” 34 But they kept silent, for on the way they had discussed with one another which of them was the greatest. 35 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.”
In that context, Jesus declares himself to be the ultimate first-last kind of leader. This is comparable to Jesus's lesson about the seat of honor...
Luke 14:7-11 (NASB)
7 And He began speaking a parable to the invited guests when He noticed how they had been picking out the places of honor at the table, saying to them, 8 “When you are invited by someone to a wedding feast, do not take the place of honor, for someone more distinguished than you may have been invited by him, 9 and he who invited you both will come and say to you, ‘Give your place to this man,’ and then in disgrace you proceed to occupy the last place. 10 But when you are invited, go and recline at the last place, so that when the one who has invited you comes, he may say to you, ‘Friend, move up higher’; then you will have honor in the sight of all who are at the table with you. 11 For everyone who exalts himself will be humbled, and he who humbles himself will be exalted.”
...That was at a wedding feast, which there also is in Revelation 20:4-6, named in 19:9...
Revelation 19:9 (NASB)
Then he said to me, “Write, ‘Blessed are those who are invited to the marriage supper of the Lamb.’” And he said to me, “These are true words of God.”
So, that kind of honor is mentioned many times in the context of being honored at a wedding feast. Jesus offered himself as the Lamb and is now the most honored person at the wedding since he is the bridegroom.
Jesus was working from the beginning and reaping the harvest at the end. He is servant of all, seated last to be honored first at the banquet, and leader of all—putting himself last and therefore being placed first above all kings.
Does this relate to time? Absolutely! Review John 1, same author...
John 1:1-3 (NASB)
1 In the beginning was the Word, and the Word was with God, and the Word was God. 2 He was in the beginning with God. 3 All things came into being through Him, and apart from Him nothing came into being that has come into being.
Now, bearing in mind the other occasions when Jesus spoke these words, reading about these things in Revelation will not only be easier to understand, but looking at Revelation as Jesus's own elaboration we can understand those previous passages better also ('first and last' language from Isaiah 41:4; 44:6, 48:12 notwithstanding).