Wise can notify you by email, WhatsApp, push (through the mobile app), and text. Which of these are turned on, and for which events, is entirely up to your institute — there's no single standard setup across all institutes, so it's worth checking with your admin to find out exactly what's enabled for your role rather than assuming.
Notifications generally fall into a few categories: session reminders at various times before a session, alerts when a session is updated or starts, chat message notifications and unread-chat digests, fee-related updates, and course activity. Any of these could be on, off, or limited to certain channels depending on how your institute has set things up.
The ones you'll most commonly want to have on: you're notified whenever a new student is assigned to you, and whenever a session is scheduled, cancelled, or rescheduled — these are usually the notifications that matter most day to day.
If you're not getting a notification you expect — like a reminder well ahead of a session — that's most likely a configuration choice rather than a bug. Ask your admin what's enabled so you know what to expect.