https://wiki.ffo.jp/html/4739.html
Levels can only increase one at a time, you can't skip from level 1 to 3 immediately by paying more.
After leveling up, it won't level up to the next tier until 1 hour 5 mins of the current level has passed. However, at the same time, a timer starts once a new level has been reached after the 1 hour 5 min mark which reduces the gil spent over the cap for the level to 0 every second. If that reaches 0, it levels down.
So, to go from 1 to 3; spend 10k or more to get level 2, wait 1 hour 5 mins, immediately buy 20k worth or more of goods to get it to level 3. Wait 1 hour 5 mins. Buy 30k worth of goods to get it to level 4. Better to overpay to get the timer higher so it doesn't hit 0 and reset the level.