You do not need to purchase the lower-tier compendiums to "unlock" the higher tier ones. As your Artifact Knowledge improves, better-quality compendiums will be available to purchase.
For a practical example of how this works:
A character that is Artifact Knowledge 15 can purchase a Artifact Research Compendium: Volumes I & II. This is sent to a fresh 110 alt who only had one Knowledge Work Order complete. The alt then uses Artifact Research Compendium: Volumes I & II to get the remaining 9 levels to hit Artifact Knowledge 10. The fresh alt would then work towards 15 by completing Knowledge is Power, and then after 15, the alt would receive regular Work Orders.
In Patch 7.2, players can send higher level compendiums to alts, as the Artifact Knowledge cap goes up to level 50: Artifact Research Compendium: Volumes I-IX, Artifact Research Compendium: Volumes I-VIII, Artifact Research Compendium: Volumes I-VII, Artifact Research Compendium: Volumes I-VI, Artifact Research Compendium: Volumes I-V