Question about Sport mode in 4.6IS

[Smokeoc68]

I was driving the other day an wanted to play a bit so I switched the gear to sport mode and didn't noticed the RPM gauge jump or the vehicle gear down. I just figured I may have missed it so i put it back to automatic and then back to sport and still didn't notice the RPM gauge jump or the vehicle gear down. So then I put it in manual and went thru the gears for a while like that but was bothered by the sport mode. I got home threw it in sport mode and felt it gear down while pulling up to the drive way. Any info about the sport mode would be greatly appreciated.

Is sport mode suppose to respond like 4th gear in manual or automatic with a little kick?

Is sport mode suppose to feel like the 4th gear in automatic? (it's been a while since i shifted it so i'm a little confused)

Thanks