I have configured a Start Timer Event with recurrence set to an interval of cons

You need to republish the model every time you update the constant. If you are updating the constant via process model you could create a custom smart service to republish the model or use the "Republish Model as Different User Smartnode" (you could even use the same user that you have publishing the model with, the node offers the ability to select any user as the publisher though) available for download here in Appian Forum under the "Shared Components" record (forum.appian.com/.../all)- Smart Services or via direct link
forum.appian.com/.../summary

You need this because when you configure the timer the model creates an image with the values at design time (10 mns in this case) to record what values it will use to launch process instances. When you update the constant at runtime the model already has an image of the original values because you configured the timer at design time, that's why republishing is necessary. This is by design but can be easily worked around by the approach described above if the update of the constant is frequent.

You need to republish the model every time you update the constant. If you are updating the constant via process model you could create a custom smart service to republish the model or use the "Republish Model as Different User Smartnode" (you could even use the same user that you have publishing the model with, the node offers the ability to select any user as the publisher though) available for download here in Appian Forum under the "Shared Components" record (forum.appian.com/.../all)- Smart Services or via direct link
forum.appian.com/.../summary

You need this because when you configure the timer the model creates an image with the values at design time (10 mns in this case) to record what values it will use to launch process instances. When you update the constant at runtime the model already has an image of the original values because you configured the timer at design time, that's why republishing is necessary. This is by design but can be easily worked around by the approach described above if the update of the constant is frequent.