GS3 screen lock to home screen

GS3 on ATT. If I am in an app or in a text messaging thread and then if I push the power button or just let the screen timeout, I of course get a black screen. Now when I go back to my phone and either press the on/off button or hit the home button I get my 'lock' screen. I have my phone set to where I get this screen and then swipe it to 'open' my phone. The issue is that once I swipe the screen the phone opens back to the last app I was on. Call me crazy but that is not the behavior I want. I want my phone to always go to the home screen when I swipe. I don't want to set the phone to home screen before it times out. If I am in a text thread and then need to set the phone down I don't want to have to hit keys so it is on the home screen when it times out........
Thanks in advance.

That's strange - I'm not running the stock ROM at the moment, but when I was, if I used the Power button to wake the phone, after I input my pattern it would return me to the previous app; however, if I used the Home button to wake the phone, after I input my pattern it would take me to the main Home screen. This was with 4.1.2.
What firmware are you running?

Sent from my rooted, debloated, deodexed Sinclair ZX-80 running CM -0.001 using Tapatalk 2

Not a problem for me, but my phone running stock 4.1.1 does the same thing that op has described.

Sent from my SGH-I747M using Tapatalk 2

Running 4.1.1

Just to be clear, I am not using a pattern. Just the Swipe screen to unlock function. The only time I get the home screen after the swipe is if I was at the home screen when I push power button once or screen times out. Which is great except, if I am in an app and the screen times out or push power button so I can store phone in the pocket, I swipe screen to unlock and I am back at the app. I understand the reason of the behavior but I want the phone to always start at the home screen without jumping through hoops. May be that it is not made that way.... Just hoping there is a setting that I have missed. Thanks.

Settings / Lock screen / Lock instantly with power key needs to be unchecked

Was suggested but Lock instantly with power key is not an option.

I am beginning to think that what I want, is the ability to where anytime I unlock my phone with the screen swipe and always go to the home screen NOT the last app I was on, is not doable.

The whole point of multi-tasking is to be able to resume what you were doing...

But, with Nova Launcher you can set the home button to do any of a number of actions, including go to the "default page." With this option checked, if you power up the phone with the home button, it will first display the screen you were on last, but then go back to the home page. Personally, I prefer the standard approach, but to each his own.