That leak in the photo looks like a leak from a fresh oil change? Can you top off the transmission fluid and cross check the engine oil for level also? Hot fluid flowing to an 8" size puddle a couple of time is not that much fluid / oil?
If you find the fluid / oil level has not moved much after another one or two puddles then you need to put the dye in.
When the transmission line O-Ring on my 03 S80 T6 was sheared from a poor installation from the previous owner the trans fluid leaked quite a bit and for sometime before it started to affect the shifting. Huge trail of fluid at it's worst towards the end and again probably leaking for sometime till it was obvious.
I did not think to top off (my radar was off) and just went ahead and put in the shift kit and flushed. Use the same amount flushed as a reference to refill. It was only after still experiencing a little bump shift that I thought to carefully check the level and this after a thorough warm up. It was then that I realized it was around 1 to 1.5 quarts low before I started working on it.






