Yes, it does sound like the pot is normal. I suspect the operation is also normal.
Nobody actually makes a logarithmic pot - they are a series of linear segments. The inexpensive ones are just two segments - the first half of the rotation is something like 10K-15K linear, from 7:00 to 12:00. The rest of the rotation is a linear 85K segment. So the slope in dB suddenly gets steeper as you pass 12:00, falling to a shallow slope as you approach 5:00. The first hals works the same way, so the last part of the first half (say, 9:30 to 12:00) is a shallow slope, no more than 6dB, while the first part of the second half (12:00 to 2:30) is steeper, maybe 13dB total.
More expensive pots might have three segments, and a few pots made for recording consoles can have even more - but they are quite expensive, comparable to switched attenuators.