Jesus claims to be the savior of the whole world,
John 3:17.
This means that salvation has been provided for everyone,
Hebrews 2:9. But only those that call upon his name will be saved,
Romans 10:13.
Christ is, and can only be, the Saviour of one world, and that world is the world to come - the new heavens and earth - not this current world. This one will be destroyed by God, not saved. So therefore, Christ as the Saviour, cannot be the Saviour of everyone - only of those He had so chosen to inhabit the new world with Him. Had he not saved them, then there could be no new world, but we know that because of His promise, there must be one, and since there must be one, we know that He has saved only those who will inhabit it.
[Jhn 3:17 KJV]
17 For God sent not his Son into the world to condemn the world;
but that the world through him might be saved.
[2Pe 3:10 KJV]
10 But the day of the Lord will come as a thief in the night; in the which
the heavens shall pass away with a great noise, and the elements shall melt with fervent heat, the earth also and the works that are therein shall be burned up.
[2Pe 3:13 KJV]
13 Nevertheless we,
according to his promise, look for new heavens and a new earth, wherein dwelleth righteousness.
[Luk 18:30 KJV]
30 Who shall not receive manifold more in this present time, and in
the world to come life everlasting.
Regarding Heb 2:9, I think you should also consider 2:13, as it further defines who those of 2:9 are. The
"every man" are only those whom God gave to Jesus, which means not everyone.
[Heb 2:9 -10, 13 KJV]
9 But we see Jesus, who was made a little lower than the angels for the suffering of death, crowned with glory and honour; that he by the grace of God should taste death for every man
10 For it became him, for whom [are] all things, and by whom [are] all things, in bringing
many sons unto glory, to make the captain of their salvation perfect through sufferings.
13 And again, I will put my trust in him. And again,
Behold I and the children which God hath given me.
Regarding Romans 10:13, again, there are other verses which further explain the intent of 10:13. One other
verse is 10:10. It tells us "with the heart man believeth" and confession is made. However, Only God can
change the heart, which must happen before someone can "believeth". That change comes with/from salvation.
[Eze 36:26 KJV]
26
A new heart also will I give you, and a new spirit will I put within you: and
I will take away the stony heart out of your flesh, and I will give you an heart of flesh.
[Jer 17:9 KJV]
9
The heart [is] deceitful above all [things], and desperately wicked: who can know it?
[Rom 10:10, 13 KJV]
10 For
with the heart man believeth unto righteousness; and with the mouth confession is made unto salvation. ...
13 For whosoever shall call upon the name of the Lord shall be saved.