The 13th technology on the manual reads:
After resolving one or more powerups gained from performing a Main action, you may pay 1 cocoa to gain an additional power-up (same Action Board)
While the main action part on the manual reads:
Pay the cost in gold as shown on the selected tile and place one
of your Technology markers (wooden discs) on it to mark that
you have acquired this Technology. Refer to the Appendix for an
explanation of the ongoing benefit of each Technology tile.
After placing the Technology marker, advance once on one
temple, depending on which column the selected Technology
belongs to: for the left column, for the centre column,
for the right column
Afterwards, power up one of your workers on the Alchemy (5)
Action Board, unless you used the 3rd option when selecting the
tile (you used a single power 4 or 5 worker to place your marker
on a second-row Technology).
Therefore, you get the power-up after you have already received the technology, and advanced on a temple. Does this mean that when powering-up your die, can you immediately pay one cocoa to gain an additional power-up?
TLDR: Can you use the technology 13 power on the same die power-up you get from purchasing the technology?