Yes, staying near your phone is recommended while your listings are active on Zutopia, since trade requests must be accepted within a short, fixed time window.
Knowing this in advance helps you avoid having an active listing automatically deactivated.
The 60-Second Window
If you're looking to trade, it is best to have your phone on loud and ready to go. You have up to 60 seconds to accept any trade request. During this 60 seconds you will be notified four times: initially, then every 15 seconds, at the 15, 30 and 45 second marks. At 60 seconds you will be notified that you were too slow and your listing will be deactivated.