Salamun alaykum,
I think 2:62 applies to everyone both before and after the Quran was revealed. This verse mentions four different people, namely:
- Amanu
- Huda
- Nasara
- Sabiina
I can say that if these four groups do exactly as instructed in 2:62, if they believe in Allah, the last day and do righteous deeds, then they are Muslim, since Islam is the only way accepted by God
3:85 And whoever follows other than ISLAM as a system <DIIN>, it will not be accepted from him, and in the Hereafter he is of the losers.
22:78 And strive for God a genuine striving. He is the One who has chosen you, and He has made no hardship for you in the DIIN - MILLATA of your father IBRAHIM. He is the One who named you 'MUSLIM' from before and in this; so let the messenger be witness over you and you be witness over the people. So hold the indoctrination and contribute towards purification and hold tight to God, He is your patron. What an excellent Patron, and what an excellent Supporter.
However, in the Qur'an, the followers of the prophet Muhammad and the readers of the Qur'an are not addressed using the word Muslim especially while in giving specific instructions, for example,
Siyam
2:183 O you ALLADHINA AMANU, fasting has been decreed for you as it was decreed for those before you, perhaps you may be righteous.
Voice
49:2 O you ALLADHINA AMANU, do not raise your voices above the voice of the prophet, nor shall you speak loudly to him as you would speak loudly to each other, lest your works become nullified while you do not perceive.
and in many others verses.
And I've never seen verses that start with "Yaaayyuhal alladhina aslamu" since we are called "alladhina amanu."
So in the hierarchy, first we are all Muslim, and then when we became without doubt, and we strive with our money and our lives in the cause of God, then we are becoming Mu'minun.
49:14 The Bedouins said: "We believe <amanna>." Say: "You have not believed <tu'minu>; but you should say: 'We have submitted <aslamna>;' until belief enters into your hearts." And if you obey God and His messenger, He will not put any of your works to waste. God is Forgiver, Merciful.
49:15 Believers are those who believe in God and His messenger, then they became without doubt, and they strive with their money and their lives in the cause of God. These are the truthful ones.
So back to 2:62, alladhina amanu in that verse is refer to us, the follower of the prophet Muhammad who already strive with our money and soul, just to distinguish from other believer who follow different Rasul. Then it applied to all of us, regardless of the time.
Peace