I think the bottom and top place connections are based on the same equations, so it's not surprising that they are both incorrect.
There is no particular reason to put the contact off to the right, but the general rule of MiM caps is that they act much like transistor gates with respect to antenna violations, and while SkyWater doesn't call out any specific antenna rules related to MiM caps in their DRC deck, the general practice is to always contact from the bottom plate of the MiM cap upward, and never downward. Arrays of MiM caps then will have alternating stripes contacting (bottom, top, bottom, top, bottom, ...). Also, there are often rules about the maximum area of a bottom plate which makes it more usual for each MiM cap in an array to have its own isolated bottom plate. Again, SkyWater does not have such a rule, but I copied and modified the MiM cap drawing routines from another process that does.
Like any layout drawing tool, the parameterized cells are "helper" functions, and you are welcome to draw your own device in whatever way you prefer, as long as it passes DRC rules.