It is a big deal to end up with straight spokes. For one, the bladed spokes are meant to cut through the air, rather than working as small fan blades.

This is also where the type of nipples makes a difference.

For typical nipples that swivel on the rim, and thread onto the spoke, I personally don't hold the spoke. I let the spokes wind up while I'm truing, then unwind them as one of the last steps, with the unwinding process having little impact on the actual spoke tension and truing.

The reverse nipples that Shimano uses on the WH-6700 and WH-6800 wheels that thread into the rim are much more of a hassle because twisting the nipple to unwind the spoke would change the tension and truing. Thus, you must hold the spoke to keep it from twisting. And, there is a fair amount of friction between the spoke and nipple, so I had to remove all the spokes and grease them to get it to work right.

I can't tell from the photos online of generic wheels what you actually have. Your mechanic would know. And, the condition the wheels are in when you get them back should be obvious by looking at the spokes.