Well I ordered over 70K worth of items from Cat and she's not there (after TTing a day) but some people say it's random. Is it random or does she just show up when you've paid 70K to T.I.Y?
If ordering from catalog works, still doesn't change the fact she is random =) I have her appear so frequently in 2 weeks but some said she appear 2 months after the last time she show up. So use some tricks. I heard if she appear in your town eg: today. After pass the check, turn your in-game clock back to 6am (the same date) and she will appear again in your plaza, so you can complete all 4 checks in one day =)