Been having this problem in FIFA 18 since an nVidia driver update, and it seems to be occurring in the FIFA 19 demo as well.
I usually get a nice 60 FPS all the time (apart from menus and cutscenes, where I get 30 FPS, but that can be fixed with adaptive vsync in the nVidia Control Panel), but whenever there's one of those cinematic replays, the FPS crashes down to below 20, and stays there for a few seconds before going back to 60... usually.
Sometimes an Alt + Tab fixes things immediately, sometimes the only way to fix it is to restart the game... Basically you have to skip the replays, but sometimes even that's not enough and the FPS tanks anyway.
With FIFA 18 at least, reverting back to an ancient driver seems to fix things, however I don't want to do the same for FIFA 19. I shouldn't be having to resort to using outdated drivers in order to have stable FPS.
According to mSi Afterburner, my GPU (an nVidia GTX 960) is at around 60-70% during a match, but during replays it suddenly jumps to 100% and stays there when the FPS is low.
Turning on adaptive vsync does seem to curb the problem a bit (as in it seems to delay the drops until a bit later on in the match), but not completely, the drops happen anyway.
I don't know whether it's something EA can do about, whether it's something I can fix, whether we just have to hope nVidia releases a driver specifically for this game (that works), but in any case, something's broken, because this problem rather lowers my enjoyment of the game.