Short answer is YES the statement you made is correct.
You have to send out push notification to each device token which must be stored in your server (provider). The preferred way to send multiple notification is to not make multiple connections but reuse one to send multiple notifications. Below is the paragraph from Apple Doc
You should also retain connections with APNs across multiple notifications. APNs may consider connections that are rapidly and repeatedly established and torn down as a denial-of-service attack. Upon error, APNs closes the connection on which the error occurred