Yes, the eBay label flow or the FedEx.com label flow will show the correct rates based on input dimensions and weights, and both will show a "base rate" in transportation cost breakdowns that can be reverse engineered to determine what billable weight was used to calculate the charges.
That's how I determine the eBay FedEx dimensional weight divisors in use in my various posts.
Run a mockup or real FedEx label creation, expand the transportation cost in classic label flow (new label flow transportation cost is useless as it included the variable eBay discount), note the base rate, determine the zone (usually USPS.com zone calculator is correct for FedEx zones also - but not always), go to the FedEx Service Guide, match the base rate and zone to a weight in the chart, and you then know what weight FedEx based the charges on.
Then take that weight, divide it by the pkg LxWxH, and out pops a possible dimensional weight divisor. Drop the weight to 0.01 lb above the next lowest pound weight and repeat. That gives the range of possible divisors (because dim weight are rounded up to whole pounds for lookup).
ie: If FedEx chart says weight is 14 lbs and package is 14x14x11, then we calculate for 13.01 lbs (since that rounds up to 14lbs for calc purposes): DWD=14x14x11/13.01=165.72=166
Anyway, the only possible assumption here is that OP didn't enter the correct dimensions in the label flow (assuming they didn't matter?). Without knowing the zone and actual box size there's no way to nail it down any more, but I'm pretty sure that's how it played out.
Based on looking at the listing and what orangehound guessed/discerned, the box couldn't have been any smaller than 12x12x8 which would have shipped at actual weight (8lb) as it's greater than dim weight, but that's jamming the bell into the box with no padding at all. A 14x14x10 box would provide 1 inch all around, is a very standard available size, and a dim weight of 12 lbs which matches what OP said FedEx claimed. However, the $22 charge only correlates if a Zone 8 shipment (unless the numbers quoted in the OP include extra insurance, sig conf, or buyer's address was rural and incurred a Delivery Area surcharge.
The basic TLDNR is that yes, FedEx dim weight (and almost every surcharge) will automatically be calculated given the correct inputs.
>>I guess I better check my invoices!
Nothing to panic about unless OP provides info that demonstrates this was not user error as a result of GIGO.
(and I just did some testing that shows at least the classic label flow behaving as expected and correctly calculating rates based on dimensional weight)
