Should I use all of my turns or not?

Depends on whether you value using them now, versus later. Reasons for using it later include hoping to buy cheaper units and tech. Reasons to use it earlier include getting the income now to buy something with it (eg buy Turrets).

A techer likes - if s/he can, to start at the very beginning of the set, go towards the top of the scores list and then stay there. The reason for this is that the price of tech is highest early in the set and then steadily declines. Also the techer must grab for their land and wants to use as few turns doing so as possible. By and large this is more easily done by growing as strong as possible as quickly as possible.

An all-X Rep casher by contrast wants to hold back as much as possible. They want to avoid being grabbed - so prefer to stay landthin - and they would also prefer, as Xin says above, to be using the cash they generate (both before and after reaching their land goal) to buy when prices are lower rather than higher. In the case of tech that is later rather than earlier. Not so easy to say when turret prices will be higher or lower or food but the all-X casher hopes to carry as little military as they dare and to have as much tech as possible so tech prices are more important to them than other prices.

In general therefore if you spy a Theo techer expect to see them showing no turns unused when they checked out whereas expect the Rep casher to have a lot of unused turns.

Those are two extreme examples. Other strats and particular circumstances (an oil shortage or food buy out for example) produce different considerations. There is no one size fits all answer to your question. You have found a subject worth thinking about. :)