Are my garage door springs supposed to have some tension on them when the door is up?
Two types of garage door springs. Extension and Torsion. You have Extension.
With Extension springs, when the door is up, there is very little to no tension on the springs. As stated upthread, upon proper adjustment of the springs, the weight of the door will be counterbalanced against the tension of the springs. With the opener disconnected, the door should go up and down freely, and be counterbalanced (door should not go up or down by itself, at least not rapidly).
I've worked on both types of springs, not a big deal if you follow the proper procedures.
My tips:
Use a good ladder that is rated over the weight of you and the stuff you are carrying.
Wear a tool belt, remove the sharp pointy things from the belt and your pockets, and have a backup wrench in case you drop the main wrench.
On torsion springs DO NOT USE SCREWDRIVERS FOR WINDING BARS! Buy or make the proper tool.
Set screws on torsion springs have square heads. 8 point sockets are ideal for this.
Think through what you will be doing before you begin.
Good Luck and Be Safe.