I'm currently building a CNC Plotter robot and purchased a 1.8" TFT ST7735 Display to make a small menu for it. I have a setup with a L7805 5v tension regulator which feeds both the Arduino and a small 3.3v 662K regulator, which in turn feeds the screen. However, whenever I turn the screen on I get this weird white accent and lines (see picture), which only goes away if I start feeding the arduino via my laptop's USB while keeping the screen fed by the regulator. If I feed the screen directly from the arduino I also get this problem.
I'm using the Adafruit library and my Arduino is a clone, if that makes any difference.
Did you build this project without any reference schematic in hand? Your problem report suggests power problems but we can't see any of that, what you did.
Unless I misunderstand, you did not say under what conditions the "normal state of the screen" exists.
Please provide a link to the display you bought. We need to know if it is for 3.3V or 5V supply and data lines.
If your display is for 3.3V - as usual for these - then your effects are to be expected. Because you may feed it with 5V through your data lines.