Are you planning on creating an app with a static view or will you have some camera control where the background moves around? The answers really change a lot depending on your goals.
I personally prefer the route of least amount of work paired with most universal solution. This means that designing my apps with bleed in mind is essential. You seem to have misunderstood me earlier, as my solutions work on all aspect ratios and resolutions.
Creating full screen sized background images that fit every aspect ratio on iOS is a lot of hard work. Trying to do the same for Android is an infeasible task. Now, whether you create one image or multiple versions of an image for different aspect ratios, you’ll run into the bleed issue in either case. It’s just a matter of where the bleed is applied.
For example, if you were to create two images: 960x640px for iPhone 4S and 1136x640px for iPhone 5. If those images are used as the background and they are centered on the screen, then they cover the entire screen on their respective devices. However, when you create that 1136x640px image in your image editor, you have to fill those extra regions on the sides with something that doesn’t exist on the smaller image. Or, in other words, this would be the bleed area. If you just ignored the 960x640px image and only created the larger image to begin with, then Corona would handle that bleed instead of you in Photoshop.
Ultimately, there are as many solutions managing different aspect ratios and resolutions across devices as there are developers, so I’ll just mention a few.
If you have just a single static background, then one approach would just be to create a large image that fits within every possible display resolution that you target, but this might be a lot of work and you’d do so knowing that some parts of the image would bleed out on every device. This means that you’d have to create your image with the safe area in mind, i.e. the area that wont bleed out. You’d want to place all of your gameplay elements within the safe area to ensure that they will be visible regardless of the device.
Alternatively, you could also create the background out of multiple images. This becomes almost necessary if you want a non-static background. Take a look at these two images from Jetpack Joyride (Image 1 & Image 2). Image 1 is a screenshot of the game on a phone and image 2 is on a tablet. The background is simply a series of images placed after one another on the x-axis. All of those images are created tall enough so that they accommodate tablets. On more narrow phone devices, those top and bottom areas simply bleed out. Knowing this, the developers didn’t place any gameplay related stuff there and it doesn’t matter that it gets cut off. The UI, i.e. the distance and coin counters and the pause button are simply attached to the top left and top right corners of the screen, so they are resolution independent.
Creating backgrounds like this means that some parts of your images/background will be cut out, but it will be the non-essential parts. If you opened the game on iPhone X, then you’d simply see additional images (tiles) on the x-axis. I also included iPhone 4s and iPhone X screenshots of one endless level select module that I’ve created. It is still using the prototype images, but you’ll get the point. In this case, I’ve locked the ground to the bottom of the screen and the clouds to the top of the screen. If I were to run this on a tablet, then the only thing that would get extended is the sky itself, so in this particular case, nothing would technically bleed out. This design is also future proof, unless we get those banana screens that Nick was talking about 
I hope this wall of text helped you out.
