Reversed position of the coil makes no difference but the correct way to install is with the lugs away from the coil stop. Now had the wires been reversed, the fuse would blow when you would flip a few times. Meaning the hold and power wiring is reversed. Holding using the power coil will blow the fuse.

Compare the left flipper coil to the right. The lugs have either a thick or thin copper wire going into the coil. The (common) lug has two wires. The thick wire is the power winding and the yellow wire goes to that lug. The hold winding is the thin wire and the orange wire goes to that lug. The red wire goes to the common lug with 2 wires.

Once the wiring is straightened out, check the mechanical aspect of the flipper. Make sure the sleeve is clean, plunger free of gunk and no burrs at the end. Check the coil stop isn't mushroomed and there is some up/down play in the flipper bat. Also make sure all the screws holding the bushing are present and tightened. There may be other things to check, but start with this and go from there.