First of all I would say don'tcha rather than dontcha. (Because of the nestled don't in there.) But I'm not sure which of those is wrong.
However the possessive of a plural does not always work like you said. For instance, "The mice's burrowing noises bothered me."
The American rule is much simpler in this regard. If you have to add the s to make the possessive, put ' before the s. Otherwise add it after the s. That covers both fans' and mice's.
Cheers,
Ben