By not adjusting for mash temp, I am assuming that you have the box to account for equipment temperature unchecked. While this works well for some systems, it does not take into account the thermal mass of the mash tun when making its calculations for strike temperature. So when you preheat the mash tun to above your strike temperature, you now have both the water and the mash tun at your strike temperature and using that combined mass and temperature to bring the grist load up to mash temp.
What I do for my BIAB system is to check the box, Set the mash tun temperature on the mash tab to the desired mash temperature, now adjust the temperature of the mash tun to the strike temperature (this may take a couple of iterations, as adjusting the temperature will affect your strike temp. Once you have done this a couple of times, it will pretty much become easy to see the offset you need to set the equipment temperature from strike temperature to bring you close enough. I generally hit my mash temperature within a few tenths of a degree F (about a tenth of a degree C).
When I use my mash tun, I just let the program calculate the entire temperature rise for both the grain and mash tun and it works very well. It took a couple of brews to get the specific heat of the mash tun set correctly, since it is a combination of metal fittings and false bottom combined with a plastic Gott-style cooler. Here also, once dialed in correctly, it brings me to within a tenth or two F of my target mash temp.