Does their fortitude take effect? If so is it only when they're deployed?
I don't have a lot of time to explain in detail, but:
Fortitudes which work against heroes work the moment the hero in the bastion gets deployed.
Fortitudes which improve the base will not work, even when the hero comes out of the bastion.
After much testing, I found all the fortitudes work except those that buff buildings. The hero must be deployed out of the bastion for the fortitude to take effect.
For example, if blockhead is in reserve, and opponent drops one hero and gets blockhead out of the bastion, when the opponents next heroes are deployed, the ground will be covered in mud. However, even if Pan Goli is in reserve and deployed, towers do not get the invulnerability buff when they reach 0 hp (same for all building buff fortitudes).