Correct, you can not make fastpass in advance at 2 different parks. All 3 in advance need to be in the same park and yes, only 1 can be tier 1 if its a tiered park, which I guess is all of them except MK.
Your other choices are to make one or two in one park in advance( one of which can be tier one) then you can get a tier one in another park same day if available. Our favorite thing to do is just use our three fastpasses in the first park, then when we tap into the 3rd ride, we immediately start looking for our fourth fastpass either in the same park or a different park since we park hop every day.
Also if you will be in Epcot as your 2nd park, just start searching for Test Track or Soarin after yountap into your 3rd advance fastpass. If Test track is important to you look for that first, we have found it easy to pick up multiple extra fastpasses for Soarin, and sometimes even the standby line is only 15 min., its a little harder for Test track but we have done it, but then again we go in May when its a little less crowded.