The master switch aka the stackmaster only needs to be set up with the config. It will then replicate this config (including STP settings) each time a new member switch joins the stack.
But in a sense, as @lagapides says here - Cisco Stackwise, we aren’t configuring the master, but the stack as a whole because it functions as a single logical switch unit.
The master manages the data plane, control plane and management plane for the stack. Any changes made in these areas are replicated to each member switch. This ensures that in the event of the existing master switch failing, a member switch can take over as the replacement stackmaster (once a re-election has occurred).
The control plane in particular manages protocols such as routing, VTP, Etherchannel, CDP, STP etc.
The network will see the stack as a single switch node with one Bridge ID in regards to rapid-pvst.
@lagapides also confirms this in response to Abishek - Cisco Stackwise
The official Cisco guide provides further info - https://www.cisco.com/c/en/us/support/docs/switches/catalyst-3750-series-switches/71925-cat3750-create-switch-stks.html#anc8
Hope this helps.