Psa 139:16  Your eyes saw my unformed substance; in your book were written, every one of them, the days that were formed for me, when as yet there was none of them. 

Psalms 139:16 is typically read as if it is describing a book in which every day of every person’s life is written from all eternity.

A person’s days are numbered in advance and recorded in God’s book “when none of them as yet existed” (Ps. 139: 16; 31: 15; 39: 5; Job 14: 5).

Bavinck, Herman. Reformed Dogmatics : Volume 2 (p. 318). Baker Publishing Group. Kindle Edition.

Gregory Boyd offers four reasons that the determinist reading of this text is not given:

First, even if this verse said that the exact length of our lives was settled before we were born, it wouldn’t follow that everything about our future was settled before we were born, and certainly not that it was settled from all eternity. God can at some point predetermine and/or foreknow some things about the future without eternally predetermining and/or foreknowing everything about the future. We must be careful not to outrun what Scripture teaches.

Second, the fact that the literary form of this verse is poetry should strongly caution us against relying on it to settle doctrinal disputes. The point of this passage is to poetically express God’s care for the psalmist from his conception, not to resolve metaphysical disputes regarding the nature of the future.

Third, the Hebrew in this passage is quite ambiguous. yamtsar) First, the word translated in the NRSV as “formed” (can be interpreted in a strong sense of “determined” or in a weaker sense of “planned.” Second, the subject matter of what was “formed” and written in the “book” before they existed is not supplied in the original Hebrew. It is thus not clear whether what was planned were the days of the psalmist’s life or rather parts of the psalmist’s body. The King James Version is an example of a translation that decided on the latter meaning. It reads, “Thine eyes did see my substance, yet being unperfect; and in thy book all my members were written, which in continuance were fashioned, fashioned, when as yet there was none of them” (Ps. 139:16). Though this wording is a bit awkward, it has the advantage of being consistent with the rest of this psalm and especially with the immediate context of this verse. Psalm 139 is about God’s moment-by-moment, intimate involvement in our lives. The verses immediately preceding verse 16 describe the formation of the psalmist’s body in the womb. Indeed, the first stanza of verse 16, “Your eyes beheld my unformed substance,” also concerns the intimate awareness the Lord has of the psalmist even before he’s formed. An interpretation of this verse that continues this theme seems most appropriate, whereas one that inserts an unrelated reference to the psalmist’s future seems out of place.

Finally, even if we choose to take the subject matter of what is “formed” and “written” in this verse to be the days of the psalmist’s life (not the parts of his body), this does not require us to believe that the length of his life was unalterable. Scripture elsewhere suggests that what is written in the Lord’s Book of Life can be changed (Exod. 32:33; Rev. 3:5). Hezekiah’s success in getting the Lord to “add” fifteen years to his life supports this perspective (Isa. 38:1–5), as does the Lord’s self-professed willingness to alter decrees he’s made in light of new circumstances (Jer. 18:6–10). The notion that what God ordains is necessarily unalterable is foreign to the Hebrew mind.

Boyd, Gregory A.. God of the Possible: A Biblical Introduction to the Open View of God (pp. 40-41). Baker Publishing Group. Kindle Edition.

John Calvin, surprisingly, takes the view that this verse is not about predestined days, but about fetology:

16. …Interpreters are not agreed as to the second clause. Some read ימים, yamim, in the nominative case, when days were made; the sense being, according to them — All my bones were written in thy book, O God! from the beginning of the world, when days were first formed by thee, and when as yet none of them actually existed. The other is the more natural meaning, That the different parts of the human body are formed in a succession of time; for in the first germ there is no arrangement of parts, or proportion of members, but it is developed, and takes its peculiar form progressively.

Calvin’s Commentaries, Vol. 12: Psalms, Part V, tr. by John King, [1847-50], at sacred-texts.com Psalm 139

In short, there is good evidence, even from Calvinistic sources, as to why this verse is not a prooftext for determinism.