They shouldn't. Encouraging notifications like Focus and Calm are designed to happen after the streak – once you are out of the Calm or Focus streak.
See, during streaks of Calm or Focus, Spire will not surface any notifications. When those streaks are over, Spire can be set to surface a notification. This is so that you can have positive, encouraging feedback about when you were doing these things so you remember what it feels like to be calm or focused.By reinforcing streaks of Calm and Focused, you strengthen your own internal compass that senses your state of mind. This is another example of how Spire helps you develop a 'sixth sense' by being not only aware of your breath but also your state of mind.