it would be helpful to the community if you expanded a bit on a few things ... 1. make/model of phone 2. a more in-depth description of the issue you're having 3. any circumstances present when you first experienced the issue
It seems you hit on all possibilities for sure.. having done 90-100 screen replacements on iPhone 7s thus far, every 10th one it seems there tends to be an issue with the home button not fully functioning as it is intended -we basically do the repairs at a snails pace now. Admittedly, once we switched to a higher quality screen, the occurrences dropped significantly, but didn't go away all together. It's a tough spot to be in but fortunately if you have some soldering experience, YouTube is being flooded with videos of seemingly competent technicians fixing certain issues involving iPhone 7 home buttons. Know your abilities and repair at your own risk. https://youtu.be/rwznLFI1Ylo https://youtu.be/lJgv6SdNsm8
i'm going to have to agree with the quality of screen as the culprit in this situation. after the second instance in our shop with an iPhone 7 screen replacement causing, what seemed to be, a shorted circuit between the home button flex and the new assembly, we bit the bullet and began using original refurbished replacement screens.
the power button on the idol 3 can be finicky as they are prone to failing. they ARE soldered to the circuit board so I would advise finding a local electronics repair shop or good friend with minimal soldering experience- seeing as the actual replacement is as simple a solder job as one could imagine . the component replacement, itself, is about $8.00 online. http://www.ebay.com/itm/Alcatel-One-Touch-Idol-3-6045-OT6045-Power-Button-Flex-Cable-On-Off-Key-/171029243190?hash=item27d2232536:g:AhoA...
you have a couple of options to choose from and considering you have opened the iPad Mini already to replace your part; - did you alter the two lens assembly magnets in anyway? (located top right and bottom right on device, usually attached to factory lens assembly) - make sure they have kapton tape covering them (or the original tape that covers said magnets) - go to settings: tweak the lock screen options, you may have to just swallow the bullet and turn it to off, but when you put a magnetized iPad cover on, it will not lock as it should. I've a bit that power button flex replacement parts tend to be lackluster quality as far as Apple products go. good luck, guy who works on iPads alot.
perhaps the tech who repaired your phone, left a screw or piece of glass (from your previous lens) and it's lodged between the LCD and some other internal component . pressing the home button down may be causing the pressure spot you're experiencing. i'd take care of it ASAP so no permanent damage is done to the LCD.
i will say replacing the battery with multiple new ones around the shop helped me for a day or two then back to the same thing. i've yet to put a new battery cover on to try out a new set of contacts from a new power button flex, that'll be my next move.