It’s true that the standard approach in Japan is to draw first and record the voices later. At first, this was strictly for budget reasons. In the 60s, it was cheaper to do things this way and as there was a massive demand to be met, the studios simply opted for the fastest and cheapest way to put films out.
This, however, ended up affecting the entire creative process, even when deadlines weren’t so strict and budgets so tight. Unlike American films, Japanese animators will make sometimes substantial changes to the script as they’re drawing it. Much of the acting is also decided before voices are recorded.
That said, though, that’s not really the reason why mouth movements don’t often follow dialog very well. This has entirely to do with budget, as it’s possible to adjust the mouth movements later; if there is enough time and money. Usually, there isn’t. (Anyway, it’s a point of detail. For most people, all Disney movies are post-dubbed because most people don’t watch them in English.)
The fact is that Japanese animated films are made on shoestring budgets. In many cases, this show, a lot. In other cases, it’s incredible how much Japanese animators can milk out of their budgets. Here are production budgets, for comparison:
The Lion King (1994) $45,000,000
Pocahontas (1995) $55,000,000
Mulan (1998) $90,000,000
Lilo and Stitch (2002) $80,000,000
Akira (1988) $10,000,000
Ghost in the Shell (1995) $6,000,000
Spirited Away (2002) $20,000,000
Steam Boy (2004) $24,000,000
Paprika (2006) $3,000,000
Steam Boy is notorious for how long it took to make and its relatively huge budget. And yet, it was still only a little over 1/4 of Lilo and Stitch’s cost. It still looked great.
Far more impressive, though, is the work of Satoshi Kon. Paprika only cost about 3 million dollars to make. That’s a little over the budget for a single Simpsons episode.