You definitely need to use dt, not to fix this issue, but to make sure your game runs correctly on different framerates.
Does this problem happen on PC, in preview? You probably have to wait longer than 2 minutes.
Does it still happen if you touch the mobile screen from time to time? Perhaps the phone detects no user activity and lowers the framerate or enters some kind of battery-saving mode.
There could also be a problem with offsetting the image in tiledbackground too far. Try this:
TiledBackground: Set image X offset to (Self.ImageOffsetX-60×dt)%Self.ImageWidth