There seems to be a growing argument for mid foot clear placement to help you run better off the bike. I would recommend sliding your cleat back on your shoe. Ride it the same for both bikes. You may need to make a very slight saddle adjustment depending on if you point your toes through the bottom of the pedal stroke.

I have started to read about some cyclists moving more toward mid foot clear placement as well.

YMMV.

Most folks use the same for both.

As mentioned, some folks have been using a further back (aka "midfoot") position. This is more popular in Tri/TT than road riding, since it's harder to sprint with a midfoot cleat than a ball-of-foot one (which is a bigger issue in road racing).

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I do wonder why the bike fitter wanted to move your cleats forward for a tri fit, as it's been said above usually it's either the same, or moved back for triathlon, saving the calves for the run.

I have separate shoes for triathlon and road bike, but use the exact same cleat setups, I haven't found cleat placement to be a limiting factor, and have gotten super comfortable with where mine are after years of riding.

Only reason I have separate shoes for in a triathlon is to get it on and off quickly, but will train in my road setup shoes most of the time.

As a long time fitter, while the bike geometries are slightly different, the biomechanics of pedaling are essentially the same. Unless the person has some sort of physical issue, road or Tri, as close to mid foot as possible.

I also prefer more midfoot position. There used to be a Speedplay kit to move the cleats more rearward. Unfortunately this kit has been discontinued. Anybody knows why?
Sam