I don't have any experience with the import $15 reamer but 4 points.
1) The grooves in the reamer are spiral, not circular, so one complete turn cuts every element of the taper.
2) When you "ream" to clean up an existing taper, only remove the high spots. Don't worry about 100% cleanup of remnants of low defects.
3) Turn the reamer by hand using a wrench or socket. Use light pressure on the reamer and your socket should clean right up.
4) Now that the socket is cleaned up, you need to check every male tool before you use it again and stone off all high spots.
Nothing to be afraid of here.