How and why do wake vortices come together to form two tip vortices?
The picture in your question is an oversimplification. Maybe this photo of an MD-11 on a moist day will help to illustrate the point:



I also think you should not call the wake vortices "tip vortices". The tip vortices are an insignificant part of the whole wake system and can be seen in the picture above on both the winglets and the horizontal tail as thin lines of condensation. The wake vortices are the result of the vorticity shed over the wingspan rolling up. With flaps set for landing, the MD-11 has a big change in circulation at the flap tips, so here the shedding is intensified and shows as a thick line of condensation. There is more going on left and right of that thick line, but it is not visible because the gradient of circulation over span is too shallow to cause condensation in the wake (it does over the wing itself, due to the low pressure on the top side).

Maybe it will be best for understanding wake rollup if you watch it happen in a video. It should also help to confirm your theory :-). A good one is at 3:20 and again at 5:40. Also, watch how the wake changes when ground effect kicks in at around 4:00.