gerbers get exported differently according to your eagle DFM settings, which you configure prior to generating gerbers— sometimes with settings provided by your manufacturer ie oshpark.
so, yes, there may be some overlaps with the mill layer, but the DFM settings should create spacing so shorts don’t happen given minimum distances. this is one of the helpful things that eagle does, if you set it up right, and know how to use it.
secondarily, a good PCB manufacturer will have an engineer review your files prior to printing. most have automated software to spot common/likely mistakes.