The healing that the Tree of Life provides, which is for the nations, occurs simultaneously whenever and, more specifically to the point of your question, wherever the Great Commission of Matthew 28:19-20 is successfully declared (understanding that success is defined by actual making of disciples, coupled with a baptism, followed by proper observation of all that the Lord Jesus commanded His Apostles through their teaching).
Matthew 28:19-20 (ESV),
19 Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, 20 teaching them to observe all that I have commanded you. And behold, I am with you always, to the end of the age.”
Note the highlighted word above, namely nations.
In Greek, the word is ethnos, meaning people joined together by a common culture and custom, which in turn makes them a nation.
In Revelation 22:2, the reference to the nations is found to be the same Greek word, that is, ethnos.
The healing of these nations takes place, in and through the Gospel, when it is preached and taught, received and obeyed, by individual members of those nations.
Isaiah 53:4-5 (ESV),
4 Surely he has borne our griefs
and carried our sorrows;
yet we esteemed him stricken,
smitten by God, and afflicted.
5 But he was pierced for our transgressions;
he was crushed for our iniquities;
upon him was the chastisement that brought us peace,
and with his wounds we are healed.
Simon Peter quotes from this passage in his epistle:
1 Peter 2:24 (ESV),
24 He himself bore our sins in his body on the tree, that we might die to sin and live to righteousness. By his wounds you have been healed.
In Isaiah 53:5, the Hebrew word for "healed" is rapha.
In 1 Peter 2:24, the Greek word for "healed" is iaomai, related to the Greek word therapeúō in the follow sense:
[2390 /iáomai ("to heal") draws the attention to the Lord, the supernatural Healer, i.e. beyond the physical healing itself and its benefits (as with 2323 /therapeúō).]
The LXX of Isaiah 53:5 uses the same Greek word as 1 Peter 2:24:
5 αὐτὸς δὲ ἐτραυματίσθη διὰ τὰς ἀνομίας ἡμῶν καὶ μεμαλάκισται διὰ τὰς ἁμαρτίας ἡμῶν παιδεία εἰρήνης ἡμῶν ἐπ' αὐτόν τῷ μώλωπι αὐτοῦ ἡμεῖς ἰάθημεν
So, in Revelation 22:2, we see the benefits of the healing that the leaves of the Tree of Life have to offer, and we see the recipients of those benefits, namely the nations, or ethnos of the world, whenever they receive the Lord Jesus and the Gospel of His salvation (as prophesied in Isaiah 53), whenever and wherever the Great Commission is achieved.
Acts 8:26-40 (ESV),
26 Now an angel of the Lord said to Philip, “Rise and go toward the south to the road that goes down from Jerusalem to Gaza.” This is a desert place. 27 And he rose and went. And there was an Ethiopian, a eunuch, a court official of Candace, queen of the Ethiopians, who was in charge of all her treasure. He had come to Jerusalem to worship 28 and was returning, seated in his chariot, and he was reading the prophet Isaiah. 29 And the Spirit said to Philip, “Go over and join this chariot.” 30 So Philip ran to him and heard him reading Isaiah the prophet and asked, “Do you understand what you are reading?” 31 And he said, “How can I, unless someone guides me?” And he invited Philip to come up and sit with him. 32 Now the passage of the Scripture that he was reading was this:
“Like a sheep he was led to the slaughter
and like a lamb before its shearer is silent,
so he opens not his mouth.
33 In his humiliation justice was denied him.
Who can describe his generation?
For his life is taken away from the earth.”
34 And the eunuch said to Philip, “About whom, I ask you, does the prophet say this, about himself or about someone else?” 35 Then Philip opened his mouth, and beginning with this Scripture he told him the good news about Jesus. 36 And as they were going along the road they came to some water, and the eunuch said, “See, here is water! What prevents me from being baptized?” 38 And he commanded the chariot to stop, and they both went down into the water, Philip and the eunuch, and he baptized him. 39 And when they came up out of the water, the Spirit of the Lord carried Philip away, and the eunuch saw him no more, and went on his way rejoicing. 40 But Philip found himself at Azotus, and as he passed through he preached the gospel to all the towns until he came to Caesarea.
Do you see how, through the prophet Isaiah, specifically chapter 53, Philip was able to teach the Gospel to an individual member of a specific nation, namely, Ethiopia, and upon receiving and believing it, this Ethiopian national agreed to baptism, and thus, the Great Commission was fulfilled?
This is how, when, and where, the leaves of the Tree of Life, that is, the message of salvation, brought healing to just one of the many nations, just as Revelation 22:2 declares it is supposed to, and will, take place.
A final note: In apocalyptic symbolism, particularly the symbolism employed in Revelation, and other prophets of the Hebrew Scriptures, it is quite common to understand trees as poetic references to humans.
We can therefore understand that the Tree of Life in Revelation 22:2 is symbolically the Lord Jesus Himself. That He is the vine, or inner life of the tree, that Christians are the branches growing upon it/Him (John 15:1-5), and the fruit (of the Spirit; see Galatians 5:22-23) are the reproducing center of that tree, and the leaves* (the message of salvation) can be used as salves or poultices (In these last two examples, note 1.) how the Greek for salve derives from kollaó, which often denotes "in ancient medical language of the uniting of wounds". And 2.), how the poultice made for King Hezekiah was derived from figs, a clear association with the fig and fig leaves of Genesis 3:7).
*In Revelation 22:2, the Greek word for "leaves" is phullon, from the word phule.
Then note that the Greek word for tribe, often used in Revelation (and elsewhere), is phule.
Note the connection. The leaves which are for the healing of the nations in Revelation 22:2 is derived from the word which refers to tribes of people, particularly the tribes of Jacob/Israel (e.g. Revelation 21:12), but also, all the various tribes of the earth (Revelation 7:9, 11:9, 13:7, and especially 14:6; see footnote referenced below as "Eternal Gospel"). As such, tribe is synonymous with ethnos, that is, an ethnos or nation is the coming together of all the various tribes found in one geographical location, for better of for worse.
This proves conclusively that the leaves of the Tree of Life are like a poultice, a panacea compound made up of the Vine (the Lord Jesus) the Branches (Christians), their fruit (of the Spirit), and finally, the Leaves (the Eternal Gospel Message of Salvation given to the tribes of the earth through the Twelve Tribes of the Israel of God) that all come together to produce the Great Commission and the fulfilling thereof, in and among, the nations.