The short answer is: you shouldn’t care about that.

There is no proper way to exit the app, i.e. terminate its process. As a PC user you’re used to close the app when you’re done with it, but mobile operating systems are different. On the Android you don’t exit the app, you leave it. That’s why it doesn’t matter if you hit the home or back button. Well, actually it does, because hitting the home button will save the app state, so it’s even better. Anyway, in both cases the app will be moved to background an will sit there until you open it again or your device will run out of free RAM. In the second case, Android’s memory management will kill the process to make room for a new app. If you really want to release resources eaten by the app, remove it from recents. That will do the job.

If you renamed, copied or moved the folder to another location, Android’s media scanner needs to scan the files again. That may take a while, so that’s why you don’t see the real size yet. Once the scan is complete, after you refresh the directory you’ll see the real folder size.

It’s also worth noting, that sometimes folder size can be innacurate. It fully depends on Android’s media scanner and on how many files it actually scanned. Anyway, in most cases folder size calculation seems to be accurate.

If you still see the folder as empty even after waiting some time, there must be something wrong with Android’s files database. This problem is not related to Solid Explorer and can’t be fixed inside the app.

This is unfortunately a bug in Android: https://code.google.com/p/android/issues/detail?id=18624

If you’re running Android Lollipop or higher, you need to grant write access to Solid Explorer. Prior to attempt to write anything you’ll see a popup asking you to select the root folder of SD Card and tap the Select button at the bottom. If you don’t see your SD Card in the sidebar, look for an option to show it in the overflow menu. You can see it in action here.

If you’re running Android KitKat and your device is not rooted, you won’t be able to write to SD Card.