The main feature and the very name of the HDR technique is to allow a scene with a large range of brightness to be rendered with a reduced range of brightness. The before-after examples you posted do not illustrate this. For example in your examples, I presume the 1st and 3rd images are the "after" versions, and the 2nd and 4th images are the "before". However, the 1st and 3rd images have more, not less, contrast than the 2nd and 4th images. The changes I see could easily be accomplished with conventional manipulations of a single exposure and don't derive any of the benefit that a true HDR treatment provides.
Take a look at the example attached below (courtesy
http://www.cambridgeincolour.com/tutorials/high-dynamic-range.htm ). This shows how two images, each with a range of brightness so large it can not be captured by a camera, can be combined into an image with a reduced range of brightness. If you want to derive the benefits of the HDR technique, this is the direction you should be trying to go in, not the opposite, ie, pumping *up* the contrast and saturation.
In addition, you mentioned changing the ISO on your phone to get a pair of images to be combined by the HDR technique. This is not the way to do it because, in most phones there is an automatic exposure system that will try to keep the exposure constant no matter how the scene brightness, ISO, etc. change. To make the HDR method work, you need at least two versions of the scene with significantly different exposures.
Finally, when you are taking multiple images you really need a means to prevent the camera from moving by even the slightest amount between exposures. Because of this, without a tripod mount, cell phones are almost impossible to use for HDR.
HTH, Tom
Tom