They should interact w/ the modes accordingly. The modes all dial in their mojo per usual just the tune amplifies the power, gets the turbos spooled sooner, & tightens the shift points etc
Same way traction & stability control & ABS will function as normal (although TC has a lot harder time reigning in the power lol)
I have a Gearhead tune & before when I was stock I pretty much exclusively drove in sport mode even when it was raining out & I needed 4A I’d put it back in sport etc. Now I just leave it in normal mode majority of the time b/c it feels perfect & a lot of that has to do w/ the boost coming on way sooner & especially from the way gearhead cleans up the shift strategy in the TCM.
When you switch into sport it still holds revs/gears longer, when you switch into Baja it still shifts hard as hell & when you switch into “weather” it still cuts the power & shifts like a wussy etc.
Think of the tune as a “layering” over all the modes.