There are several intertextual clues that Matthew uses to draw parallels between the temptation scene and the commission scene.
First off, in both scenes there is a claim of authority over the nations, with a further parallel of this authority being "given":
Again the Devil took him along to an unusually high mountain and showed him all the kingdoms of the world and their glory. And he said to him: "All these things I will give you"
All authority has been given me in heaven and on the earth. Go, therefore, and make disciples of people of all the nations
Matthew undoubtedly draws these parallel to show us that Jesus has obtained what Satan offered him in chapter 4 not by worshipping Satan, but by remaining obedient to God even unto death.
A second parallel between the two scenes is that both take place on a mountain:
Again the Devil took him along to an unusually high mountain
However, the 11 disciples went to Galʹi·lee to the mountain where Jesus had arranged for them to meet.
The fact of the mountains by itself may not be too impressive, but as Gage and Carpenter have argued
1, Matthew seems to have placed these two mountains as the first and last of a seven mountain chiastic structure.
It's clear from Matthew 1 and his observation of the three sets of 14 generations that Matthew is not foreign to seeing meaning in the number seven, suggesting this set of seven mountains may not be an accident of the text. Further, the second mountain (of Sermon on the Mount fame) and the sixth mountain (home of the Olivet discourse) have strong parallels to each other with the beatitudes of the former finding a counterpart in the woes pronounced by Jesus in the latter.
This chiastic structure would place the mountain of temptation and the mountain of the great commission in parallel with each other and invite us as readers to compare the two. Reflecting on this comparison, Richard Hays writes
The devil offers Jesus all the kingdoms of the world if Jesus will only fall down and worship him (προσκυνήσεις), but Jesus repels this seduction by a ringing quotation of Deuteronomy 6:13 LXX: "The Lord your God you shall worship (προσκυνήσεις) and him alone you shall serve" (Matt 4:9-10). Once this commandment has been forcefully set forth in the narrative, readers have little choice but to interpret Jesus' acceptance of worship from other characters as an implicit acknowledgment of his divine identity.
Finally, the parallels we have drawn are further corroborated by noting Jesus' final statement in the great commission: "And look! I am with you all the days until the conclusion of the system of things." His statement that "I am with you" forms an inclusio with Matthew 1:23 and the name Immanuel, "With Us Is God", given to Jesus there. Again Hays
[I]n view of Matthew’s portrayal of Jesus as "God with us" and his use of the verb [προσκυνεῖν] in settings where it unmistakably narrates an appropriate human response to Jesus' epiphanic self-manifestation (14:33, 28:9, 28:17), it is hard to deny that, in and through these references to worshiping Jesus, Matthew is identifying him as nothing less than the embodied presence of Israel's God, the one to whom alone worship is due, the one who jealously forbids the worship of any idols, images, or other gods.
In sum, given the parallels between the temptation narrative and the great commission narrative, along with the other contextual evidence, we should interpret the use of προσκυνεῖν in both passages in the same way - as something due to God alone, and which is yet portrayed as proper to Jesus as well.
1 Gage, W. A., & Carpenter, S. P. (2014). A Literary Guide to the Life of Christ in Matthew, Mark, and Luke-Acts: How the Synoptic Evangelists Tell the Story of Jesus (p. 20). St. Andrews House.
2 Hays, Richard B.. Echoes of Scripture in the Gospels (p. 167). Baylor University Press. Kindle Edition.
3 Ibid. 167