No, that is not common. A few suggestions...take a look at the adapter...my first Sony tape adapter that came with a portable CD player had a selection switch for aligning the head for different car stereos. See if yours has one and check each selection.
Second, make sure you turn off the "Metal" tape selector on your headunit. That will affect the sound quality as the tape adapter is considered a "Normal" tape bias. Third, turn off the Dolby NR. The incoming signal from the iPod is not Dolby-encoded so that will make the sound muffled.
If those don't work, spend the $19 and buy a new tape adapter.