The vaccine instructs cells to produce a piece of protein from the spike. There’s no such thing as “a” spike protein, the spike is a structure of proteins that enable a lot of functions for the virus. They choose a piece of protein from the structure that’s antigenic then encode the mRNA to produce that. The mRNA is delivered into the cell by the lipid transport and the cell picks up the instruction and produces the antigenic protein fragment. Your immune system responds as expected and attacks the antigen carrying things - existing cells included. The inoculated mRNA is quickly broken down because mRNA is a standard process in cell function.

Unless the effect observed is due to the antigen the vaccine produces then you wouldn’t expect to see the same behavior in vaccinated humans as they saw experimentally with a full virus, even if some part or the full assembly of the spike is a cause for cellular damage.